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If 3x2+px+12=0 has equal roots, find the values ...

If 3x2+px+12=0 has equal roots, find the values of p .

A.

±12

B.

±3

C.

±4

D.

±6

Correct answer is A

The general form of a quadratic equation is:

x2-(sum of roots) = 0

For equal roots it's:x^2 - 2(α)+(α)^2=0

3x^2+px+12=0

Divide through by 3

= x^2+\frac{p}{3}x+4=0

=x^2-(-\frac{p}{3})x+4=0

So,α^2=4

= α = √4 = ±2

Also,-\frac{p}{3}= 2α

When α = 2

-\frac{p}{3} = 2(2)=4

=p=-12

When α =-2

-\frac{p}{3}=2(-2)=-4

= p = 12

∴ values of p = ±12