if p and q are the zeros of the quadratic polynomial p(x)= 4x^2-5x-1, find the value of p^2q+pq^2​

by

if p and q are the zeros of the quadratic polynomial p(x)= 4x^2-5x-1, find the value of p^2q+pq^2​

2 thoughts on “if p and q are the zeros of the quadratic polynomial p(x)= 4x^2-5x-1, find the value of p^2q+pq^2​”

  1. Step-by-step explanation:

    Given :–

    p and q are the zeros of the quadratic polynomial p(x)= 4x^2-5x-1

    To find :–

    Find the value of p^2q+pq^2 ?

    Solution :–

    Given quardratic polynomial P(x)=4x^2-5x-1

    On Comparing this with the standard quadratic Polynomial ax^2+bx+c

    We have

    a = 4

    b = -5

    c = -1

    Given that

    p and q are the zeores of P(x)

    We know that

    The sum of the zeroes = -b/a

    =>p+q = -(-5)/4

    => p+q = 5/4 ——-(1)

    and

    The product of the zeroes = c/a

    => p×q = -1/4

    => pq = -1/4 ——–(2)

    Now

    p^2q + pq^2

    => pq(p+q)

    From (1)&(2) then

    => (-1/4)(5/4)

    => (-1×5)/(4×4)

    => -5/16

    Answer:–

    The value of p^2q + pq^2 for the given problem is –5/16

    Used formulae:–

    • The standard quadratic Polynomial is ax^2+bx+c.
    • Sum of the zeores = -b/a
    • The product of the zeroes = c/a

Leave a Comment