Question

If 1 is a root of the quadratic equation 3x^2+ ax - 2 = 0 and the quadratic equation
a(x^2 + 6x ) - b = 0 has equal roots, find the value of b.​

Answer 1

Answer:

Value of b = 9

Step-by-step explanation:

Given Problem:

If 1 is a root of the quadratic equation 3x^2 + ax - 2 = 0 and the quadratic equation  a(x^2+ 6x)-b=0 has equal roots, find the value of b.​

Solution:

To Find:

Value of b.

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Method:

Since,

1 is a root of equation 3x^2 + ax - 2 = 0

We have,

⇒ 3(1)² + a (1) - 2 = 0

⇒3 + a - 2 = 0

⇒a + 1 = 0

⇒ a = -1

Now, a (x² + 6x) - b = 0    (Has equal roots.)

I.e. a x²+6a x - b = 0           (Has equal roots.)

⇒Discriminant = b²- 4 ac = 0

⇒(6a)² - 4 (a) (-b) = 0

⇒36a² + 4ab = 0

⇒36 ×(-1)² + 4 (-1)b = 0

⇒36 - 4ab = 0

⇒4b = 36

⇒b = 9

Hence,

The value of b = 9