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Maths 2 Marks Questions

Polynomials · Jharkhand Board (JAC) STD 10 (Jharkhand - English Medium). 3 questions.

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2 Marks Questions

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3 questions · self-marked practice — reveal the answer and mark yourself.

Question 12 Marks
Answer the following and justify:
Can the quadratic polynomial $x^2 + kx + k$ have equal zeroes for some odd integer $k > 1?$
Answer
Let $p(x) = x^2 + kx + k$
For equal zeroes,$ b^2 - 4ac = 0$
$\Rightarrow (k)^2 - 4(1) (k) = 0$
$\Rightarrow k^2 - 4k = 0$
$\Rightarrow k(k - 4) = 0$
$\Rightarrow k = 0 or k = 4$
But $k > 1$ so $k = 4$
The given quadratic polynomial has equal zeroes at $k = 4.$
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Question 22 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)?
Answer
When p(x) is divided by g(x), the remainder is zero so the g(x) is a factor of p(x) and degree of g(x) will be less than of equal to the degree of p(x) of degree g(x) $\leq$ degree p(x).
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Question 32 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)?
Answer
The dividend = p(x), divisor g(x)
quotient q(x) = 0
remainder = r(x)
Here, degree of divisor g(x) is more than degree of dividend.
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2 Marks Questions - Maths STD 10 Questions - Vidyadip