# alg2/trig

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If 4x^2+9=kx, what value of k will produce equal roots?

• alg2/trig -

4 x ^ 2 + 9 = kx

4 x ^ 2 - k x + 9 = 0

Quadratic equation has two real roots, if Discrininant Ä = 0

Ä = b ^ 2 - 4 * a * c

In this case :

a = 4

b = - k

c = 9

Ä = b ^ 2 - 4 * a * c

Ä = ( - k ) ^ 2 - 4 * ( 4 ) * 9

Ä = k ^ 2 - 144 = 0

k ^ 2 - 144 = 0

k ^ 2 = 144

k = sqrt ( 144 )

k = ± 12

For k = - 12

4 x ^ 2 + 9 = k x

not equal becouse left side of equation are positive ( 4 x ^ 2 + 9 ) are allways great of 0 ) ,and right side of equation are negative.

So solution are k = 12

• alg2/trig -

Quadratic equation has two real equals roots, if Discrininant Ä = 0

Ä = greek letter Delta

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