Question

find the zeros of the given polynomial and verify the relation between its zeros and coefficients 4x²+5 root 2x- 12​

Answer 1

Answer

Hey buddy !

Here is your answer : =

Polynomial is :

P(x) = 4x^2 + 5√2x - 12 ( By middle term split )

=4x^2 + ( 8√2 - 3√2 )x - 12 = 0

=4x^2 + 8√2x - 3√2x - 12 = 0

=4x ( x + 2√2 ) - 3√2 ( x + 2√2) = 0

= (4x-3√2) (x+2√2) = 0

= 4x - 3√2 = 0. x+2√2=0

= 4x = 3√2. x= -2√2

= x = 3√2/4

here, Zeroes are 3√2/4 and -2√2

Verify,,

P(x) = 4x^2 + 5√2x - 12

Here, a = 4 , b = 5√2 and c = -12

Sum of zeroes = -b/a

3√2/4 + (-2√2) = - 5√2/4

3√2/4 - 2√2 = -5√2/4

-5√2/4 = -5√2 /4

Product of zeroes = c/a

(3√2/4) (-2√2) = - 12 / 4

-12/4 = -12/4

Hence verified...

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