Question

find the quadratic polynomial if the sum and product of its zeroes is 3 and -10

Answer 1

Answer:

standard form of a quadratic polynomial is

{x^2-(sum of roots) +(product of roots) }

given sum of roots =3 , product of roots=-10

put the value in standard eq

(x^2-3x-10)

Answer 2

❏ Solution

Given :-

• Sum of zeroes = 3
• Product of zeroes = -10

Find :-

• Quadratic equation

❏ Explanation

Formula

$\star\boxed{\boxed{\tt{\blue{\:x^2-(Sum\:of\:zeroes)x\:+(Product\:of\:zeroes)\:=\:0}}}}$

Then , Now Keep all above Values,

➠ x² - (3)x + (-10) = 0

➠ x² - 3x - 10 = 0

❏ Hence

• Quadric equation be x² - 3x - 10 = 0

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Answer Verification

First find zeroes of this equation,

➠ x² - 3x - 10 = 0

Using Formula,

$\star\tt{\red{\:Sum\:of\:zeroes\:=\:\dfrac{-(coefficient\:of\:x)}{(coefficient\:of\:x^2)}}}$

$\star\tt{\blue{\:Product\:of\:zeroes\:=\:\dfrac{(constant\:part)}{(coefficient\:of\:x^2)}}}$

Let, here

• p & q are zeroes

So,

➠ Sum of zeroes = -(-3)/1

➠ p + q = -3

Again,

➠ product of zeroes = -(10)/1

➠ product of zeroes = -10

That's proved.

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