Question

Form a quadratic polynomial p(x) with 3 and -2by5 as

Answer 1

Let 3&-2/5 be alfa and beta.
P(x) = x²-(sum of zeros) x+product of zeros
P(x) =x²-{3+(-2/5)}x+3×-2/5
P(x)=x²- (3-2/5)x+(-6/5)
P(x)=x²-(15-2/5)x-6/5
P(x) =x²-13/5x-6/5
P(x)=5x²-13x-6

Answer 2

Hey there !

Solution:

Actually the question is if 3 and -2/5 are the zeros.

So proceeding with the question we get,

General form of Quadratic Polynomial is:

x² - Sum of zeros ( x ) + Product of zeros

Sum of Zeros = 3 + ( -2/5 )

Taking LCM we get,

=> 15 - 2 / 5 = 13 / 5

Product = 3 * - 2 / 5

=> Product = - 6 / 5

=> Quadratic Polynomial = x² - ( 13 x / 5 ) - ( 6 / 5 ) = 0

Taking LCM we get,

=> Quadratic Polynomial = ( 5x² - 13x - 6 ) / 5 = 0

Transposing the denominator 5 to the RHS we get,

=> Quadratic Polynomial = 5x² - 13x - 6 = 0

Hence this is the final answer.

Hope my answer helped !