Advertisements
Advertisements
Question
Find the discriminant of the following equations and hence find the nature of roots: 7x2 + 8x + 2 = 0
Advertisements
Solution
7x2 + 8x + 2 = 0
Here a = 7, b = 8, c = 2
∴ D = b2 - 4ac
= (8)2 - 4 x 7 x 2
= 64 - 56
= 8
∴ Discriminant = 8
∵ D > 0
∴ Roots are real and distinct.
APPEARS IN
RELATED QUESTIONS
Find the values of k for which the roots are real and equal in each of the following equation:
(k + 1)x2 - 2(k - 1)x + 1 = 0
What is the nature of roots of the quadratic equation 4x2 − 12x − 9 = 0?
Find the value of k for which equation 4x2 + 8x – k = 0 has real roots.
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
x2 - 4x + 1 = 0
Find the value of k so that sum of the roots of the quadratic equation is equal to the product of the roots:
kx2 + 6x - 3k = 0, k ≠ 0
Find the value of k so that sum of the roots of the quadratic equation is equal to the product of the roots:
(k + 1)x2 + (2k + 1)x - 9 = 0, k + 1 ≠ 0.
Find the values of p for which the equation 3x2 – px + 5 = 0 has real roots.
Find the value(s) of m for which each of the following quadratic equation has real and equal roots: x2 + 2(m – 1) x + (m + 5) = 0
The probability of selecting integers a ∈ [–5, 30] such that x2 + 2(a + 4)x – 5a + 64 > 0, for all x ∈ R, is ______.
Which of the following equations has two real and distinct roots?
