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real and equal roots

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by sanju09 » Mon Apr 04, 2011 2:10 am
For what value of 'm' will the quadratic equation x^2 - m x + 4 = 0 have real and equal roots?
(A) 16
(B) 8
(C) 2
(D) -4
(E) -8

[spoiler]OA D[/spoiler]
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by manpsingh87 » Mon Apr 04, 2011 3:02 am
sanju09 wrote:For what value of 'm' will the quadratic equation x^2 - m x + 4 = 0 have real and equal roots?
(A) 16
(B) 8
(C) 2
(D) -4
(E) -8

[spoiler]OA D[/spoiler]
for real and equal roots we must have D=0 i.e. b^2-4ac=0; m^2-4*4=0 m^2=16, i.e. m can be either 4 or -4, considering options we left with only -4 hence D
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by Anurag@Gurome » Mon Apr 04, 2011 3:58 am
sanju09 wrote:For what value of 'm' will the quadratic equation x^2 - m x + 4 = 0 have real and equal roots?
(A) 16
(B) 8
(C) 2
(D) -4
(E) -8

[spoiler]OA D[/spoiler]
A quadratic equation with the general form ax² + bx + c = 0 has real and equal roots if the discriminant, b² - 4ac = 0.
In the given equation, x² - mx + 4 = 0, b² - 4ac = m² - 4(1)(4) = m² - 16 = 0, which implies m² = 16 or m = +4, - 4.
-4 is the only possible choice.

The correct answer is D.
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