Q1 of 83 Page 85

Find the discriminant of the following quadratic equations and discuss the nature of the roots:

x2 — 3√3x — 30 = 0

Comparing equation x2 — 3√3x — 30 = 0 with ax2 + bx + c = 0 we get


a = 1, b = – 3√3 and c = – 30


Discriminant (D) = b2 – 4ac


⇒ D = (– 3√3)2 – 4(1)(– 30)


⇒ D = (32)(√3)2 + 120


⇒ D = 9 × 3 + 120


⇒ D = 27 + 120


⇒ D = 147


As D > 0 roots of equation x2 — 3√3x — 30 = 0 are real and distinct


More from this chapter

All 83 →
1

Find the discriminant of the following quadratic equations and discuss the nature of the roots:

x2 + 2x + 4 = 0

 1

Find the discriminant of the following quadratic equations and discuss the nature of the roots:

x2 + x + 1 = 0

 2

If a, b, c R, a > 0, c < 0, then prove that the roots of ax2 + bx + c = 0 are real and distinct.

 3

Find k, if the roots of x2 — (3k — 2)x + 2k = 0 are equal and real.