Find-the-value-of-p-and-q-that-will-make-x-4-13x-3-6x-2-px-q-a-perfect-square-

Question Number 8602 by tawakalitu last updated on 17/Oct/16

Find the value of p and q that will make

x^{4} + {13 x}^{3} + {6 x}^{2} + px + q

a perfect square

Answered by sandy_suhendra last updated on 17/Oct/16

let {(x^{2} + ax + b)}^{2} = x^{4} + {13 x}^{3} + {6 x}^{2} + px + q

so x^{4} + {2 ax}^{3} + (a^{2} + 2 b) x^{2} + 2 abx + b^{2} = x^{4} + {13 x}^{3} + {6 x}^{2} + px + q

we get \Rightarrow 2 a = 13 \Rightarrow a = 6.5

a^{2} + 2 b = 6 \Rightarrow b = - 18.125

2 ab = p \Rightarrow p = - 235.625

b^{2} = q \Rightarrow q = 328.515625

Commented by tawakalitu last updated on 17/Oct/16

Thanks so much sir