What should be subtracted to the polynomial $x^2-16 x+30$, so that $15$ is the zero of the resulting polynomial?
- A$30$
- B$14$
- ✓$15$
- D$16$
Answer: C.
View full solution →Question types
Polynomials question types
232 questions across 5 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
232
Questions
5
Question groups
5
Question types
01
M.C.Q (1 Marks)
120 Q→02True False[1 Marks ]
4 Q→032 Marks Questions
39 Q→043 Marks Question
44 Q→055 Marks Questions
25 Q→Sample Questions
Polynomials questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If one of the zeroes of a quadratic polynomial of the form $x^2+a x+b$ is the negative of the other, then it:
- ✓Has no linear term and constant term is negative.
- BHas no linear term and the constant term is position.
- CCan have a linear term but the constant term is negative.
- DCan have a linear term but the constant term is positive.
Answer: A.
View full solution →If $\alpha,\beta$ are the zeros of the polynomial $f(x) = ax^2 + bx + c$, then $\frac{1}{\text{a}^2}+\frac{1}{\beta^2}=$
- A$\frac{\text{b}^2-2\text{ac}}{\text{a}^2}$
- ✓$\frac{\text{b}^2-2\text{ac}}{\text{c}^2}$
- C$\frac{\text{b}^2+2\text{ac}}{\text{a}^2}$
- D$\frac{\text{b}^2+2\text{ac}}{\text{c}^2}$
Answer: B.
View full solution →If one of the zeroes of the quadratic polynomial $(k - 1)x^2 + kx + 1$ 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.
View full solution →Given that of the zeroes of the cubic polynomial $a x^3+b x^2+c x+d$ are $0$ , the third zero is:
- ✓$\frac{-\text{b}}{\text{a}}$
- B$\frac{\text{b}}{\text{a}}$
- C$\frac{\text{c}}{\text{a}}$
- D$\frac{-\text{d}}{\text{a}}$
Answer: A.
View full solution →If a quadratic polynomial f(x) is not factorizable into linear factors, then it has no real zero. (True/ False).
If a quadratic polynomial f(x) is a square of a linear polynomial, then its two zeros are coincident.(True/ False).
If a quadratic polynomial f (x) is not factorizable into linear factors, then it has no real zero.
If a quadratic polynomial f (x) is a square of a linear polynomial, then its two zeroes are coincident.
The graph of the polynomial $f(x)=a x^2+b x+c$ is as shown in Fig. Write the value of $b^2-4 a c$ and the number of real zeros of $f(x)$, write the sign of $c$.
View full solution →Write the standard form of a quadratic polynomial with real coefficients.
The graph of the polynomial $f(x) = ax^2 + bx + c$ is as shown in Fig. Write the value of $b^2 - 4ac$ and the number of real zeros of f(x).
View full solution →If a quadratic polynomial f(x) is factorizable into linear distinct factors, then what is the total number of real and distinct zeros of f(x)?
Write the family of quadratic polynomials having $-\frac{1}{4}$ and 1 as its zeros.
View full solution →Give an example of polynomials $f(x), g(x), q(x)$ and $r(x)$ satisfying $f(x)=g(x), q(x)+r(x)$, where degree $r(x)=0$.
View full solution →If $\alpha$ and $\beta$ are the zeroes of the quadratic polynomial $f(x) = ax^2 + bx + c$, then evaluate:$\alpha^4+\beta^4$
View full solution →For 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 factorization.
$\frac{21}{8},\frac{5}{16}$
View full solution →$\frac{21}{8},\frac{5}{16}$
If a - b, a and b are zeros of the polynomial $f(x) = 2x^3- 6x^2 + 5x - 7$, write the value of a.
View full solution →What must be added to the polynomial $f(x) = x^4 + 2x^3 - 2x^2 + x - 1$ so that the resulting polynomial is exactly divisible by $x^2 + 2x - 3?$
View full solution →For what value of k, -4 is a zero of the polynomial $x^2 - x - (2k + 2)?$
View full solution →If the zeros of the polynomial $f(x) = ax^3 + 3bx^2 + 3cx + d$ are in A.P., prove that $2b^3 - 3abc + a^2d = 0.$
View full solution →If $\alpha$ and $\beta$ are the zeros of the quadratic polynomial $f(x) = x^2 - px + q$, prove that $\frac{\alpha^2}{\beta^2}+\frac{\beta^2}{\alpha^2}=\frac{\text{p}^2}{\text{q}}-\frac{4\text{p}^2}{\text{q}}+2.$
View full solution →Find all zeros of the polynomial $f(x) = 2x^4 - 2x^3 - 7x^2 + 3x + 6$, if its two zeros are $-\sqrt{\frac{3}{2}}$ and $\sqrt{\frac{3}{2}}$
View full solution →If the zeros of the polynomial $f(x) = 2x^3 - 15x^2 + 37x - 30$ are in A.P., find them.
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