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 nature of the roots of the following quadratic equation. If the real roots exist, find them:
2x2 - 3x + 5 = 0
Find the nature of the roots of the following quadratic equation. If the real roots exist, find them:
2x2 - 6x + 3 = 0
Find the values of k for which the roots are real and equal in each of the following equation:
`kx^2-2sqrt5x+4=0`
If a, b, c are real numbers such that ac ≠ 0, then show that at least one of the equations ax2 + bx + c = 0 and -ax2 + bx + c = 0 has real roots.
Solve for x :
x2 + 5x − (a2 + a − 6) = 0
Find the value(s) of k for which the pair of equations
kx + 2y = 3
3x + 6y = 10 has a unique solution.
Without solving the following quadratic equation, find the value of ‘p’ for which the given equation has real and equal roots:
x² + (p – 3) x + p = 0
The roots of the quadratic equation `2"x"^2 - 2sqrt2"x" + 1 = 0` are:
Find whether the following equation have real roots. If real roots exist, find them.
`x^2 + 5sqrt(5)x - 70 = 0`
The sum of all integral values of k(k ≠ 0) for which the equation `2/(x - 1), 1/(x - 2) = 2/k` in x has no real roots, is ______.
