# What is the value of b if the following quadratic equation has equal roots: 4x^2 + bx + 18 =0

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The roots of a quadratic equation ax^2 + bx + c = 0 are given by x1 = [-b + sqrt (b^2 – 4ac)]/2a and x2 = [-b - sqrt (b^2 – 4ac)]/2a.

If the two roots are to be equal, sqrt (b^2 – 4ac) should be equal to 0

=> sqrt (b^2 – 4*18*4) = 0

=> b^2 – 4*18*4 = 0

=> b^2 = 4*18*4

=> b = + sqrt (4*18*4) and b = -sqrt (4*18*4)

=> b = 12*sqrt 2 and b = -12*sqrt 2

**Therefore b can be equal to 12*sqrt 2 and -12*sqrt 2**

Given that 4x^2+bx+18 = 0 is a quadratic equation whose roots are equal. To find the value of b.

If Ax^2+Bx+C = 0 has equal roots, then the discriminant D B^2-4AC = 0.

In this case A = 4, B = b and C = 18.

Therefore B^2-4AC = 0 implies b^2-4*4*18 = 0.

b^2 = 4^2*18

Therefore b = +sqrt (4^2*18) , b= - sqrt (4^2*18)

So b = 4*3sqrt2 , b = -4*3*sqrt2.

Therefore b = 12sqrt2, or b= -12sqrt2.