Question

The product of the zeros of the polynomial root 2 X square + 3 x minus root 2 is

Answer 1

$\underline{\textsf{Given:}}$

$\textsf{Polynomial is}$

$\mathsf{\sqrt{2}x^2+3x-\sqrt{2}}$

$\underline{\textsf{To find:}}$

$\textsf{Product of the zeros of the given polynomial}$

$\underline{\textsf{Solution:}}$

$\underline{\textsf{Concept used:}}$

$\textsf{For the polynomial}\;\mathsf{ax^2+bx+c}$

$\textsf{Sum of the zeros}\;\mathsf{=\dfrac{-b}{a}}$

$\textsf{Product of the zeros}\;\mathsf{=\dfrac{c}{a}}$

$\textsf{Consider,}$

$\mathsf{\sqrt{2}x^2+3x-\sqrt{2}}$

$\textsf{Product of the zeros}\;\mathsf{=\dfrac{c}{a}}$

$\textsf{Product of the zeros}\;\mathsf{=\dfrac{-\sqrt{2}}{\sqrt{2}}}$

$\textsf{Product of the zeros}\;\mathsf{=\dfrac{-1}{1}}$

$\implies\boxed{\textsf{Product of the zeros}\;\mathsf{=-1}}$

Find more:

Obtain other zeroes of the polynomial

f(x) = 2x4 + 3x3 - 5x2 - 9x - 3

if two of its zeroes are √3 and - √3.​

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If a and b are the zeros of polynomial 6x²-(k+1)-7x such that one zero is 11/6 more than the other, find the value of k.

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