Question

if x^4+4x^3-7x^2+kx+l is a perfect square then find k and l.please solve it fast

Answer 1

Lets say the expression is of the form $(x^{2} + bx + c) ^{2}$
Expand it -> $x^{4} + 2b x^{3} + ( b^{2} + 2c) x^{2} + 2bcx + c^{2}$

Now compare the coefficients
2b = 8 -> b = 4
$b^{2} + 2c = -7$ -> c = $- \frac{11}{2}$

Now,
k = 2bc -> k = -22
l = $c^{2}$ -> l = $\frac{121}{4}$