Question

find a quadratic polynomial such that sum of zeros is zero and product of zero is 7​

Answer 1

$\large\underline{\pmb{\frak{Given....}}}$

Given that, the product and sum of the zeroes of a quadratic polynomial are 0 and 7.

$\large \underline{\pmb{\frak{To~ find....}}}$

Wr have to find the quadratic polynomial.

$\large \underline{\pmb{\frak{Solution....}}}$

Here, according to the question :

$\qquad➺$ Sum of the zeroes (α+β) = 7

$\qquad➺$ Product of the zeroes (αβ) = 0

We know that :

$\qquad➺$ Polynomial : $\sf x^2- (\alpha + \beta) x + (\alpha\beta)$

$\qquad \sf ➺~ x^2- (7) x + (0)$

$\qquad \sf➺ ~x^2 - 7x$

_____________________

Therefore, the required quadratic polynomial is x² - 7x.