Question

find the zeros of the quadratic polynomial x²+7x+10 and verify relationship between the zeros and the coefficients​

Answer 1

Given :

• A quadratic polynomial x² + 7x + 10 .

To Find :

• Zeroes of the polynomial and verify the relationship between the zeroes and the coefficients .

Solution :

$\longmapsto\tt\bf{{x}^{2}+7x+10=0}$

By Splitting Middle Term :

$\longmapsto\tt{{x}^{2}+(5x+2x)+10=0}$

$\longmapsto\tt{{x}^{2}+5x+2x+10=0}$

$\longmapsto\tt{x(x+5)+2(x+5)=0}$

$\longmapsto\tt{(x+5)\:\:(x+2)=0}$

• x = -5
• x = -2

So , -5 and -2 are the zeroes of Quadratic Polynomial x² + 7x + 10 .

Here :

• a = 1
• b = 7
• c = 10

Sum of Zeroes :

$\longmapsto\tt{\alpha+\beta=\dfrac{-b}{a}}$

$\longmapsto\tt{-5+(-2)=\dfrac{-7}{1}}$

$\longmapsto\tt{-5-2=-7}$

$\longmapsto\tt\bf{-7=-7}$

Product of Zeroes :

$\longmapsto\tt{\alpha\beta=\dfrac{c}{a}}$

$\longmapsto\tt{-5\times{-2}=\dfrac{10}{1}}$

$\longmapsto\tt\bf{10=10}$

HENCE VERIFIED

Answer 2

Answer:

Given :-

A quadratic polynomial x² + 7x + 10 .

To Find :-

Relationship between zero

Solution :-

We know that

x² + 7x + 10 = 0

x² + 5x + 2x + 10

x(x + 5) + 2(x + 5) = 0

(x + 5) (x + 2) = 0

• x = -5
• x = -2

Sum of the zeroes

α + β = -b/a

-5 + -2 = -7/1

-7 = -7/1

-7 = -7

Now,

Product of zeroes

αβ = c/a

-5 × -2 = 10/1

10 = 10