Advertisements
Advertisements
प्रश्न
Discuss the nature of the roots of the following quadratic equations : -2x2 + x + 1 = 0
Advertisements
उत्तर
-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
संबंधित प्रश्न
Solve for x : ` 2x^2+6sqrt3x-60=0`
Find the values of k for which the quadratic equation (k + 4) x2 + (k + 1) x + 1 = 0 has equal roots. Also find these roots.
Find the nature of the roots of the following quadratic equation. If the real roots exist, find them:
2x2 - 6x + 3 = 0
Find the value(s) of k so that the quadratic equation 3x2 − 2kx + 12 = 0 has equal roots ?
Form the quadratic equation whose roots are:
`2 + sqrt(5) and 2 - sqrt(5)`.
In each of the following, determine whether the given numbers are roots of the given equations or not; 3x2 – 13x – 10 = 0; 5, `(-2)/(3)`
Discuss the nature of the roots of the following equation: 3x2 – 7x + 8 = 0
Find the values of k so that the quadratic equation (4 – k) x2 + 2 (k + 2) x + (8k + 1) = 0 has equal roots.
If the coefficient of x2 and the constant term of a quadratic equation have opposite signs, then the quadratic equation has real roots.
Assertion (A): If one root of the quadratic equation 4x2 – 10x + (k – 4) = 0 is reciprocal of the other, then value of k is 8.
Reason (R): Roots of the quadratic equation x2 – x + 1 = 0 are real.
