Question

solve:
x²+5x-(a²+a-6)=0
by b²-4ac=0 method.....♪​

Answer 1

Step-by-step explanation:

solution:-

the given equation is x²+5x-(a²+a-6)

comparing it with ax²+bx+c=0 we get

a=1 ,b=5 and c= -(a²+a-6)

find discriminant

D=b²-4ac =(5)²-4×1×-(a²+a-6)=25+4(a²+a-6)

=25+4a²+4a-24

D=4a²+4a+1

now factories D

4a²+4a+1

=4a²+2a+2a+1

=2a(2a+1)+1(2a+1)

=(2a+1)(2a+1)

D=(2a+1)²

to find the value of x use quadratic formula

$x = \frac{ - b \pm \sqrt{d} }{2a}$

$x = \frac{ - 5 \pm \sqrt{(2a + 1) {}^{2} } }{2 \times 1}$

$x = \frac{ - 5 \pm(2a + 1)}{2}$

$x = \frac{ - 5 + 2a + 1}{2} \: and \: \frac{ - 5 - 2a - 1}{2}$

$x = \frac{2a - 4}{2} \: \: and \: \: \frac{ - 6 - 2a}{2}$

$x = \frac{2(a - 2)}{2} \: and \: \frac{ - 2(3 + a)}{2}$

hence,(a-2) and -(3+a) are the root of the given equation