Advertisements
Advertisements
प्रश्न
Find the roots of the quadratic equation by using the quadratic formula in the following:
2x2 – 3x – 5 = 0
Advertisements
उत्तर
The quadratic formula for finding the roots of quadratic equation
ax2 + bx + c = 0, a ≠ 0 is given by,
x = `(-b +- sqrt(b^2 - 4ac))/(2a)`
∴ x = `(-(-3) +- sqrt(3^2 - 4(2)(-5)))/(2(2))`
= `(3 +- sqrt(49))/4`
= `(3 +- 7)/4`
= `5/2, -1`
APPEARS IN
संबंधित प्रश्न
If the quadratic equation px2 − 2√5px + 15 = 0 has two equal roots then find the value of p.
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:
x2 - 4kx + k = 0
In the following determine the set of values of k for which the given quadratic equation has real roots:
2x2 − 5x − k = 0
Show that the equation 2(a2 + b2)x2 + 2(a + b)x + 1 = 0 has no real roots, when a ≠ b.
Find the value of the discriminant in the following quadratic equation :
10 x - `1/x` = 3
Determine the nature of the roots of the following quadratic equation :
(x - 1)(2x - 7) = 0
Find the value(s) of k for which the pair of equations
kx + 2y = 3
3x + 6y = 10 has a unique solution.
`10x -(1)/x` = 3
`(2)/x^2 - (5)/x + 2` = 0
Solve for x : `9^(x + 2) -6.3^(x + 1) + 1 = 0`.
If a is a root of the equation x2 – (a + b)x + k = 0, find the value of k.
Find the discriminant of the following equations and hence find the nature of roots: 7x2 + 8x + 2 = 0
Find the discriminant of the following equations and hence find the nature of roots: 3x2 + 2x - 1 = 0
Without solving the following quadratic equation, find the value of ‘p’ for which the given equations have real and equal roots: x2 + (p – 3)x + p = 0.
Find the value (s) of k for which each of the following quadratic equation has equal roots : kx2 – 4x – 5 = 0
Find the value(s) of p for which the equation 2x2 + 3x + p = 0 has real roots.
The value of 'a' for which the sum of the squares of the roots of 2x2 – 2(a – 2)x – a – 1 = 0 is least is ______.
The roots of equation (q – r)x2 + (r – p)x + (p – q) = 0 are equal.
Prove that 2q = p + r; i.e., p, q, and r are in A.P.
Which of the following equations has imaginary roots?
