Question

the value of a such that x^2-11x+a=0,x^2-14x+2a=0 may have an common root is
​

Answer 1

Step-by-step explanation:

Let α be common root.

Given eqaution:

x2−11x+a=0 and x2−14x+2a=0

′α′ satisfies both the equation.

α2−11α+a=0 and

α2−14α+2a=0

−22a−(−14a)α2=a−2aα=−14−(−11)1

⇒−8aα2=−aα⇒α=8

Putting value of α in equation we get,

82−11×8+a=0

⇒−24+a=0

⇒a=24