Advertisements
Advertisements
Question
Find the roots of the quadratic equation by using the quadratic formula in the following:
2x2 – 3x – 5 = 0
Advertisements
Solution
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
RELATED QUESTIONS
Solve for x : ` 2x^2+6sqrt3x-60=0`
If `x=2/3` and x =−3 are roots of the quadratic equation ax2 + 7x + b = 0, find the values of a and b.
Find the values of k for which the roots are real and equal in each of the following equation:
x2 - 2kx + 7k - 12 = 0
Find the values of k for which the roots are real and equal in each of the following equation:
(k + 1)x2 - 2(k - 1)x + 1 = 0
Find the values of k for which the given quadratic equation has real and distinct roots:
kx2 + 6x + 1 = 0
If the roots of the equation (b − c) x2 + (c − a) x + (a − b) = 0 are equal, then prove that 2b = a + c.
Show that the equation 2(a2 + b2)x2 + 2(a + b)x + 1 = 0 has no real roots, when a ≠ b.
Determine the nature of the roots of the following quadratic equation :
x2 -4x + 4=0
Solve the following quadratic equation using formula method only
`"x"^2 + 1/2 "x" = 3`
Find the value(s) of k for which the pair of equations
kx + 2y = 3
3x + 6y = 10 has a unique solution.
ax2 + (4a2 - 3b)x - 12 ab = 0
Find the value of k for which the given equation has real roots:
9x2 + 3kx + 4 = 0.
If one root of the quadratic equation ax2 + bx + c = 0 is double the other, prove that 2b2 = 9 ac.
Find the value(s) of m for which each of the following quadratic equation has real and equal roots: x2 + 2(m – 1) x + (m + 5) = 0
What is the value of discriminant for the quadratic equation X2 – 2X – 3 = 0?
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:
Find whether the following equation have real roots. If real roots exist, find them.
–2x2 + 3x + 2 = 0
If b = 0, c < 0, is it true that the roots of x2 + bx + c = 0 are numerically equal and opposite in sign? Justify.
Find the value of 'p' for which the quadratic equation p(x – 4)(x – 2) + (x –1)2 = 0 has real and equal roots.
Find the value of k for which the roots of the quadratic equation 5x2 – 10x + k = 0 are real and equal.
