Polynomials - Jharkhand Board (JAC) STD 10 Maths Questions

Q 1M.C.Q (1 Marks)1 Mark

Choose the correct answer from the given four options in the following questions:The number of polynomials having zeroes as -2 and 5 is:

A
1.
B
2.
C
3.
✓
More than 3.

Answer: D.

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Q 2M.C.Q (1 Marks)1 Mark

Choose the correct answer from the given four options in the following questions:
The zeroes of the quadratic polynomial $\text{x}^2+\text{kx}+\text{k},\text{ k}\neq0,$:

✓
Cannot both be positive.
B
Cannot both be negative
C
Are always unequal.
D
Are always equal.

Answer: A.

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Q 3M.C.Q (1 Marks)1 Mark

Choose the correct answer from the given four options in the following questions:
If the zeroes of the quadratic polynomial $ax^2 + bx + c, c ≠ 0$ are equal, then:

✓
c and a have opposite signs.
B
c and b have opposite signs.
C
c and a have the same sign.
D
c and b have the same sign.

Answer: A.

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Q 4M.C.Q (1 Marks)1 Mark

Choose the correct answer from the given four options in the following questions:A quadratic polynomial, whose zeroes are –3 and 4, is:

A
$x^2-x+12$.
B
$x^2+x+12$.
✓
$\frac{x^2}{2}-\frac{x}{2}-6$
D
$2 x^2+2 x-24$.

Answer: C.

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Q 5M.C.Q (1 Marks)1 Mark

Choose the correct answer from the given four options in the following questions:If one of the zeroes of the quadratic polynomial $(k-1) x^2+k x+1$ is -3 , then the value of $k$ is:

✓
$\frac{4}{3}$
B
$\frac{-4}{3}$
C
$\frac{2}{3}$
D
$\frac{-2}{3}$

Answer: A.

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Q 6True False[1 Marks ]1 Mark

Are the following statements 'True' or 'False'? Justify your answers.
If two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant terms.

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Q 7True False[1 Marks ]1 Mark

Are the following statements 'True' or 'False'? Justify your answers.
If the graph of a polynomial intersects the x-axis at only one point, it cannot be a quadratic polynomial.

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Q 8True False[1 Marks ]1 Mark

Are the following statements 'True' or 'False'? Justify your answers.
If all the zeroes of a cubic polynomial are negative, then all the coefficients and the constant term of the polynomial have the same sign.

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Q 9True False[1 Marks ]1 Mark

Are the following statements 'True' or 'False'? Justify your answers.
If the zeroes of a quadratic polynomial $ax^2 + bx + c$ are both positive, then a, b and c all have the same sign.

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Q 10True False[1 Marks ]1 Mark

Are the following statements 'True' or 'False'? Justify your answers.
If all three zeroes of a cubic polynomial $x^3+a x^2-b x+c$ are positive, then at least one of $a, b$ and $c$ is non-negative.

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Q 111 Marks Question1 Mark

Answer the following and justify:
Can $x^2-1$ be the quotient on division of $x^6+2 x^3+x-1$ by a polynomial in $x$ of degree 5 ?

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Q 121 Marks Question1 Mark

Answer the following and justify:
What will the quotient and remainder be on division of $a x^2+b x+c$ by $p x^3+q x^2+r x+s, p \neq 0$ ?

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Q 132 Marks Questions2 Marks

Answer the following and justify:
Can the quadratic polynomial $x^2 + kx + k$ have equal zeroes for some odd integer $k > 1?$

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Q 142 Marks Questions2 Marks

Answer the following and justify:
If on division of a non-zero polynomial p(x) by a polynomial g(x), the remainder is zero, what is the relation between the degrees of p(x) and g(x)?

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Q 152 Marks Questions2 Marks

Answer the following and justify:
If on division of a polynomial p(x) by a polynomial g(x), the quotient is zero, what is the relation between the degrees of p(x) and g(x)?

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Q 163 Marks Question3 Marks

Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
$3x^2 + 4x – 4.$

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Q 173 Marks Question3 Marks

Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
$5t^2 + 12t + 7.$

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Q 185 Marks Questions5 Marks

Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
$2\text{x}^2 +\frac{7}{2}\text{x}+\frac{3}{4}$.

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Q 195 Marks Questions5 Marks

Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
$7\text{y}^2-\frac{11}{3}\text{y}-\frac{2}{3}$.

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Q 205 Marks Questions5 Marks

For each of the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also find the zeroes of these polynomials by factorisation.
$-2\sqrt{3},-9$

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Q 215 Marks Questions5 Marks

For each of the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also find the zeroes of these polynomials by factorisation.
$\frac{-8}{3}$, $\frac{4}{3}$

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Q 225 Marks Questions5 Marks

Find $k$ so that $x^2+2 x+k$ is a factor of $2 x^4+x^3-14 x^2+5 x+6$. Also find all the zeroes of the two polynomials.

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