Advertisements
Advertisements
Question
Discuss the nature of the roots of the following quadratic equations : -2x2 + x + 1 = 0
Advertisements
Solution
-2x2 + x + 1 = 0
Here a = -2, b = 1, c = 1
∴ D = b2 - 4ac
= (1)2 - 4 x (-2) x 1
= 1 + 8
= 9
∵ D > 0
∴ Roots are real and distinct.
APPEARS IN
RELATED QUESTIONS
Solve the following quadratic equation using formula method only
`"x"^2 + 1/2 "x" - 1 = 0`
For what values of k, the roots of the equation x2 + 4x +k = 0 are real?
Find the values of k so that the sum of tire roots of the quadratic equation is equal to the product of the roots in each of the following:
kx2 + 2x + 3k = 0
In each of the following, determine whether the given numbers are roots of the given equations or not; x2 – 5x + 6 = 0; 2, – 3
Find the values of k so that the quadratic equation (4 – k) x2 + 2 (k + 2) x + (8k + 1) = 0 has equal roots.
If `1/2` is a root of the equation `"x"^2 + "kx" - (5/4)` = 0 then the value of k is:
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(x – 1)(x + 2) + 2 = 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 ______.
If α, β are roots of the equation x2 + px – q = 0 and γ, δ are roots of x2 + px + r = 0, then the value of (α – y)(α – δ) is ______.
Find the value of ‘c’ for which the quadratic equation
(c + 1) x2 - 6(c + 1) x + 3(c + 9) = 0; c ≠ - 1
has real and equal roots.
