Question

If $x^2+7x+1=0and(a^2-4a)x+bx-3=0$ have both the roots in common, then find the value of a

• A. 3
• B. 1
• C. 4
• D. 2

Answer 1

Answer: (A), (B)

The correct options are
A

3

B

1

If two equations have the same roots or represent the same equation, then the ratio of the corresponding

Coefficients is same

$x^2$ + 7x + 1 = 0

and

($a^2$ - 4a)x + bx - 3 = 0

Represent the same equation

$\Rightarrow$ We can compare the coefficients.

$\Rightarrow$ $\frac{a^2-4a}{1}$ =$\frac{b}{7}$ = $\frac{-3}{1}$

$\uparrow$ ------------------- $\uparrow$

$\Rightarrow$ $a^2$ - 4a = -3

$a^2$ - 4a + 3 = 0

$\Rightarrow$ (a - 3) (a - 1) = 0

$\Rightarrow$ a = 1 or a = 3