Question

solve the quadratic equation using formula​

Answer 1

Step-by-step explanation:

This implies that

x2+2ax=4x−4a−13

or

x2+2ax−4x+4a+13=0

or

x2+(2a−4)x+(4a+13)=0

Since the equation has just one solution instead of the usual two distinct solutions, then the two solutions must be same i.e. discriminant = 0.

Hence we get that

(2a−4)2=4⋅1⋅(4a+13)

or

4a2−16a+16=16a+52

or

4a2−32a−36=0

or

a2−8a−9=0

or

(a−9)(a+1)=0

So the values of a are −1 and 9.

Answer 2

Answer:

$a = 2 \\ b = 5 \\ c = - 2 \\ \frac{ - b + \sqrt{(b ) {}^{2} - 4ac} }{2a} \\ \frac{ - 5 + \sqrt{ {5}^{2} - 4 \times 2 \times (- 2)} }{2 \times 2} \\ = \frac{ - 5 + \sqrt{25 + 16} }{4} \\ = \frac{ - 5 + \sqrt{41} }{4}$

$\frac{ - b - \sqrt{(b) {}^{2} - 4ac } }{2a} \\ \frac{ - 5 - \sqrt{ {5}^{2} -4 \times 2 \times ( - 2) } }{2 \times 2} \\ = \frac{ - 5 - \sqrt{25 + 16} }{4} \\ = \frac{ - 5 - \sqrt{41} }{4}$