Question

Find the value (s) of k, if the quadratic equation 3x
^2-k root3x+4+9 has equal roots.

Answer 1

You can solve this 2 ways:

1) trying to fit it into the pattern of the square of a binomial (“completing the square”) to look like (x+y)2=x2+2xy+y2(x+y)2=x2+2xy+y2

2) remembering that a quadratic equation has 2 equal real roots when the discriminant is zero, so Delta=b2–4ac=0Delta=b2–4ac=0

For 1) rewrite the equation, dividing both sides by 3:

x2−k3–√x3+43=0⟹x2−kx3–√+43=0x2−k3x3+43=0⟹x2−kx3+43=0

…which would correspond to the square:

(x±23–√)2=x2±2(x)(23–√)+43(x±23)2=x2±2(x)(23)+43

…and comparing coefficients of x from last line, this leads to k=±4k=±4

For solution 2) you will have 3k2−48=0⟹k=±