For what values of p are the roots of the equation 4x2 + px + 3 = 0 r

1.	For what values of p are the roots of the equation 4x2 + px + 3 = 0 real-and equal?
Answer» 4x² + px + 3 = 0 Compare given equation with the general form of quadratic equation, which is ax² + bx + c = 0 a = 4, b = p, c = 3 Find discriminant: D = b² – 4ac = p² – 4 x 4 x 3 = p²- 48 Since roots are real and equal (given) Put D = 0 p² – 48 = 0 p² = 48 = (±4√3)² p = ± 4√3 Hence p= 4√3 or p = -4√3

For what values of p are the roots of the equation 4x2 + px + 3 = 0 real-and equal?

Answer»

4x² + px + 3 = 0

Compare given equation with the general form of quadratic equation, which is ax² + bx + c = 0

a = 4, b = p, c = 3

Find discriminant:

D = b² – 4ac

= p² – 4 x 4 x 3

= p²- 48

Since roots are real and equal (given)

Put D = 0

p² – 48 = 0

p² = 48 = (±4√3)²

p = ± 4√3

Hence p= 4√3 or p = -4√3