Question

If x2+2x+1=0 and x2+ax+9=0 has one common root then the value of a is

Answer 1

Answer:

a = 10

Step-by-step explanation:

Given a quadratic equation such that,

${x}^{2} + 2x + 1 = 0$

To find it's roots, we need to factorise it.

Therefore, we will get,

$= > {x}^{2} + 2 \times x \times 1 + {1}^{2} = 0 \\ \\ = > {(x + 1)}^{2} = 0 \\ \\ = > x + 1 = 0 \\ \\ = > x = - 1$

Therefore, the root is -1.

Now, given another quadratic equation,

${x}^{2} + ax + 9 = 0$

But, it's given that,

The root of first eqn is also common for the second eqn.

Therefore, it will satisfy the second eqn also.

Therefore, substituting the value, we get,

$= > {( - 1)}^{2} + a( - 1) + 9 = 0 \\ \\ = > 1 - a + 9 = 0 \\ \\ = > 10 - a = 0 \\ \\ = > a = 10$

Hence, required value of a = 10.