Question

if 3x-4 is a factor of the polynomial p(x)=2x³-11x²+kx-20, find the value of k​

Answer 1

Solution

Given :-

• (3x - 4) is a factor of Equation, p(x) = 2x³ - 11x² kx - 20 .

Find :-

• Value of k

Explantion

We know,

If, (x-a) be a factor of Equation, ax² + bx + c = 0,

then, x = a , satisfied this Equation for the value of x.

So, If we here

Take , 3x - 4 = 0, Or, x = 4/3,

This, value satisfied this Equation 2x³ - 11x² kx - 20 .

So, keep x = 4/3.

==> 2 × (4/3)³ - 11 × (4/3)² + k × 4/3 - 20 = 0

==> 2 × 64/27 - 11 ×16/9 + 4k/3 = 20

==> 4k/3 = 20 + 176/9 - 128/27

==> 4k = 20×3 + 176×3/9 - 128×3/27

==> 4k = 60 + 176/3 - 128/9

Take L.C.M. of 1,3 & 9

==> 4k = ( 60 × 9 + 176 × 3 - 128)9

==> 4k = ( 540 + 528 - 128)/9

==> 4k = ( 1068 - 128)/9

==> 4k = (940)/9

==> k = 940/(9×4)

==> k = 235/9

Hence

• Value of k will be = 235/9

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Answer 2

Answer:

Step-by-step explanation: