Advertisements
Advertisements
प्रश्न
If a = 1, b = 4, c = – 5, then find the value of b2 – 4ac
उत्तर
b2 – 4ac = (4)2 – 4(1)(– 5)
= 16 + 20
= 36
APPEARS IN
संबंधित प्रश्न
Find that non-zero value of k, for which the quadratic equation kx2 + 1 − 2(k − 1)x + x2 = 0 has equal roots. Hence find the roots of the equation.
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 values of k for which the roots are real and equal in each of the following equation:
4x2 + kx + 9 = 0
Find the values of k for which the roots are real and equal in each of the following equation:
kx(x - 2) + 6 = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
2x2 + kx + 3 = 0
If the roots of the equation (b - c)x2 + (c - a)x + (a - b) = 0 are equal, then prove that 2b = a + c.
Solve for x :
x2 + 5x − (a2 + a − 6) = 0
Solve the following quadratic equation using formula method only
16x2 - 24x = 1
48x² – 13x -1 = 0
In each of the following determine the; value of k for which the given value is a solution of the equation:
x2 + 2ax - k = 0; x = - a.
Determine whether the given quadratic equations have equal roots and if so, find the roots:
x2 + 2x + 4 = 0
Find the discriminant of the following equations and hence find the nature of roots: 2x2– 3x + 5 = 0
Which of the following equations has 2 as a root?
Which of the following equations has no real roots?
If one root of the equation x2+ px + 12 = 0 is 4, while the equation x2 + px + q = 0 has equal roots, the value of q is:
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?
Find the value(s) of 'a' for which the quadratic equation x2 – ax + 1 = 0 has real and equal roots.
If b and c are odd integers, then the equation x2 + bx + c = 0 has ______.
Complete the following activity to determine the nature of the roots of the quadratic equation x2 + 2x – 9 = 0 :
Solution :
Compare x2 + 2x – 9 = 0 with ax2 + bx + c = 0
a = 1, b = 2, c = `square`
∴ b2 – 4ac = (2)2 – 4 × `square` × `square`
Δ = 4 + `square` = 40
∴ b2 – 4ac > 0
∴ The roots of the equation are real and unequal.
If one root of the quadratic equation 3x2 – 8x – (2k + 1) = 0 is seven times the other, then find the value of k.
