If 2 and $- \frac{1}{2}$ is the sum and product of the zeros of the polynomials respectively then the quadratic polynomial f(x) is:

x^{2} - 2 x - 4

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4 x^{2} - 2 x + 1

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2 x^{2} + 4 x - 1

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2 x^{2} - 4 x - 1

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Solution

The correct option is B $2 x^{2} - 4 x - 1$
Let say $α$ , $β$ be the zeros of the quadratic polynomial $a x^{2} + b x + c$ , then

$(α + β) = 2 = - \frac{b}{a}, α β = - \frac{1}{2} = \frac{c}{a}$

If $a = 2$ , then $b = - 4$ , and $c = - 1$
Therefore the required polynomial will be $2 x^{2} - 4 x - 1$ .

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Similar questions

Q. Finding the square root of the polynomial

4 x^{4} + 8 x^{3} + 8 x^{2} + 4 x + 1.

Q. Is the following quadratic polynomial reducible or irreducible?

f (x) = - 2 x^{2} - 2 x - 1

If $α$ and $β$ are the zeroes of the quadratic polynomial $f (x) = x^{2} - 2 x + 1$ , then find a quadratic polynomial whose zeroes are $\frac{2 α}{β}$ and $\frac{2 β}{α}$

Q. If

f (x)

is a quadratic polynomial such that graph of

y = f (x)

touches at

(4, 0)

and intersects the positive

y -

axis at

4

, then which of the following is/are correct?

Q. If

α

and

β

are the zeroes of polynomial,

f (x) = x^{2} - 2 x - 3,

then find new quadratic polynomial having zeroes

\frac{1}{α} a n d \frac{1}{β} .

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If 2 and −12 is the sum and product of the zeros of the polynomials respectively then the quadratic polynomial f(x) is:

The correct option is B 2x2−4x−1Let say α, β be the zeros of the quadratic polynomial ax2+bx+c , then (α+β)=2=−ba,αβ=−12=caIf a=2, then b=−4, and c=−1Therefore the required polynomial will be 2x2−4x−1.

If 2 and $- \frac{1}{2}$ is the sum and product of the zeros of the polynomials respectively then the quadratic polynomial f(x) is: