Question

The sum and the product of the zeroes of the polynomial in y are 3 and -10 respectively . find the quadratic polynomial

Answer 1

$\huge \fcolorbox{red}{pink}{Solution :)}$

Given ,

Sum of roots = 3

Product of roots = -10

We know that , the quadratic polynomial is given by

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

Substitute the known values , we get

➡(x)² - 3x + (-10)

➡(x)² - 3x - 10

Hence , the required polynomial is

Hence , the required polynomial is (x)² - 3x - 10

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Answer 2

Given:-

Sum of Zeroes=3

(α+β)=3

Product of Zeroes=-10

(α×β)=-10

To find:-

The Quadratic Polynomial?

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$\blue{\boxed{\orange{\underline{\red{\mathrm{Proof:-}}}}}}$

•using Quadratic Formula,

→k[x²-(sum of zeroes)x+product of zeroes]

→k[x²-(α+β)x+αβ]

•Putting in the Given Values↓

→k[x²-(3)x+(-10)

→k[x²-3x-10]

Let k=1

→x²-3x-10 is The Quadratic Polynomial.

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