Question

If 5x6−9x2+1=(px4+qx3+rx2+sx+t)(ax2+bx+c) , then the value of ap is​

Answer 1

Answer:

answer is 5

Step-by-step explanation:

Solution:

(px4+qx3+rx2+sx+t)(ax2+bx+c)

By multiplying x4  coefficient in px4+qx3+rx2+sx+t  and x2  coefficient  in ax2+bx+c  we get apx6

5x6=apx6

ap=5

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Answer 2

$\sf If \: 5 {x}^{6} - 9 {x}^{2} + 1 = (p {x}^{4} + q {x}^{3} + r {x}^{2} + sx + t )(a {x}^{2} + bx + c )$

then value of ap = 5

Given :

The equation

$\sf 5 {x}^{6} - 9 {x}^{2} + 1 = (p {x}^{4} + q {x}^{3} + r {x}^{2} + sx + t )(a {x}^{2} + bx + c )$

To find :

The value of ap

Solution :

Step 1 of 2 :

Write down the given equation

The given equation is

$\sf 5 {x}^{6} - 9 {x}^{2} + 1 = (p {x}^{4} + q {x}^{3} + r {x}^{2} + sx + t )(a {x}^{2} + bx + c )$

Step 2 of 2 :

Equate the coefficient of $\sf {x}^{6}$ in both sides

$\sf 5 {x}^{6} - 9 {x}^{2} + 1 = (p {x}^{4} + q {x}^{3} + r {x}^{2} + sx + t )(a {x}^{2} + bx + c )$

$\sf \implies \: 5 {x}^{6} - 9 {x}^{2} + 1 = ap {x}^{6} + (bp + aq ){x}^{5} +(cp + a r ){x}^{4} + (cq + br) {x}^{3} +(cr + b s) {x}^{2} + (t b + cs)x + ct$

Equating the coefficient of $\sf {x}^{6}$ in both sides we get ap = 5

Hence the required value of ap = 5

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