Question

Find the zeros of the quadratic polynomial x² + 7x + 10, and verify the relationship between the zeros and the coefficients.

Answer 1

Dear Student:

The zeros of the quadratic polynomial x² + 7x + 10,  are -2 and -5.

See the attachment for zeros and relationship between coefficient and zeros.

Answer 2

Solution :

Let p(x) = x²+7x+10

We get zeroes of the polynomial

p(x) we will take p(x) = 0

=> x² + 7x + 10 = 0

=> x² + 2x + 5x + 10 = 0

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

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

=> x + 2 = 0 or x + 5 = 0

=> x = -2 or x = -5

Therefore

The zeroes of p(x) are -2 , -5

i ) Compare x²+7x+10 with ax²+bx+c

we get

a = 1 , b = 7 , c = 10

Sum of the zeroes = - 2 + ( -5 )

= -7

= ( -b/a )

ii ) Product of the zeroes

= ( -2 )( -5 )

= 10

= c/a

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