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
Find the values of k for the following quadratic equation, so that they have two equal roots.
2x2 + kx + 3 = 0
Find the value of k for which the equation x2 + k(2x + k – 1) + 2 = 0 has real and equal roots.
Find the value of k for which the following equation has equal roots.
x2 + 4kx + (k2 – k + 2) = 0
Determine the nature of the roots of the following quadratic equation:
`3/5x^2-2/3x+1=0`
Find the values of k for which the roots are real and equal in the following equation:
x2 – 4kx + k = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
2x2 + kx + 2 = 0
If the roots of the equation (a2 + b2)x2 – 2(ac + bd)x + (c2 + d2) = 0 are equal, prove that `a/b = c/d`.
Find the value(s) of k for which each of the following quadratic equation has equal roots: (k + 4)x2 + (k + 1)x + 1 =0 Also, find the roots for that value (s) of k in each case.
If the roots of equation 3x2 + 2x + (p + 2) (p – 1) = 0 are of opposite sign then which of the following cannot be the value of p?
Compare the quadratic equation `x^2 + 9sqrt(3)x + 24 = 0` to ax2 + bx + c = 0 and find the value of discriminant and hence write the nature of the roots.
