If 2 is a root of the equation x2-b x-12-0 and the equation x2-b x-q-0 has equal roots- then q-a 8b -8c 16d -16

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Standard X

Mathematics

Nature of Roots

If 2 is a roo...

Question

If 2 is a root of the equation x² + bx + 12 = 0 and the equation x² + bx + q = 0 has equal roots, then q =

(a) 8
(b) −8
(c) 16
(d) −16

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Solution

2 is the common roots given quadric equation are , and

Then find the value of q.

Here, ….. (1)

….. (2)

Putting the value of in equation (1) we get

Now, putting the value of in equation (2) we get

Then,

As we know that

Putting the value of

The given equation will have equal roots, if

Thus, the correct answer is

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If 2 is a root of the equation x2 + bx + 12 = 0 and the equation x2 + bx + q = 0 has equal roots, then q = (a) 8 (b) −8 (c) 16 (d) −16

If 2 is a root of the equation x² + bx + 12 = 0 and the equation x² + bx + q = 0 has equal roots, then q =

(a) 8
(b) −8
(c) 16
(d) −16