Question

if the sum of the zeros is - 1, and their product is 7, then find the quadratic polynomial​

Answer 1

$\large{\underline{\underline{\mathfrak{\green{\sf{Solution:-}}}}}}$.

$\large{\underline{\underline{\mathfrak{\pink{\sf{Give\:Here:-}}}}}}$.

✴Sum of Zeros. = -1.

✴Product of Zeros = 7.

$\large{\underline{\underline{\mathfrak{\green{\sf{Find\:Here:-}}}}}}$.

✴$\red{\:Quadratic\:Equation}$.

$\large{\underline{\underline{\mathfrak{\green{\sf{Explanations:-}}}}}}$.

➡We know that .

$\green{\:Formula\:of\:Quadratic\:Equation}$.

✴$\red{\:X^2-X(\:Sum\:of\:zeros)\:+\:(\:product\:of\:zeros)\:=\:0}$.

$\implies\:X^2-X(-1)+(7)\:=\:0$.

$\implies\:X^2+X+7\:=\:0$.

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Answer 2

$\mathtt{ \huge{ \fbox{SOLUTION : }}}$

Given ,

Sum of zeroes = - 1

Product of zeroes = 7

We know that , the quadratic equation is given by

$\sf \large \fbox{ {(x)}^{2} - (sum \: of \: roots)x + (product \: of \: roots) = 0}$

Substitute the values , we obtain

$\sf \hookrightarrow {(x)}^{2} - ( - 1)x + 7 = 0 \\ \\ \sf \hookrightarrow {(x)}^{2} + 1x + 7 = 0$

Hence , (x)² + x + 7 is the required polynomial