Question

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Answer 1

Question :

Find the value of alpha for which the equation

(α-12) x²+2(α-12)x+2=0 has equal real roots .

Theory :

For a Quadratic equation of the form

ax²+bx+c= 0 , the expression b²-4ac is called the discriminant.

Nature of roots

The roots of a quadratic equation can be of three types.

If D>0, the equation has two distinct real roots.

If D=0, the equation has two equal real roots.

If D<0, the equation has no real roots.

Solution :

We have to find the value of α for which the quadratic (α-12) x²+2(α-12)x+2=0 has equal real roots.

Let (α-12) = a

So, ax²+2ax+2=0.

We know that, When roots are equal,if Discriminant = 0

Then ,

⇒b²-4ac= 0

⇒(2a)²-4(a)(2)=0

⇒4a²-8a=0

⇒4(a-2)=0

⇒a-2=0

⇒a=2

Thus, a =(α-12)

⇒α-12=2

⇒α=14

Hence, Value of α is 14 if the equation (α-12)x ²+ 2( α-12) x + 2 =0 have equal roots.

Answer 2

Question :

Find the value of alpha for which the equation

(α-12) x²+2(α-12)x+2=0 has equal real roots .

Theory :

For a Quadratic equation of the form

ax²+bx+c= 0 , the expression b²-4ac is called the discriminant.

Nature of roots

The roots of a quadratic equation can be of three types.

If D>0, the equation has two distinct real roots.

If D=0, the equation has two equal real roots.

If D<0, the equation has no real roots.

Solution :

We have to find the value of α for which the quadratic (α-12) x²+2(α-12)x+2=0 has equal real roots.

Let (α-12) = a

So, ax²+2ax+2=0.

We know that, When roots are equal,if Discriminant = 0

Then ,

⇒b²-4ac= 0

⇒(2a)²-4(a)(2)=0

⇒4a²-8a=0

⇒4(a-2)=0

⇒a-2=0

⇒a=2

Thus, a =(α-12)

⇒α-12=2

⇒α=14

Hence, Value of α is 14 if the equation (α-12)x ²+ 2( α-12) x + 2 =0 have equal roots.