Advertisements
Advertisements
प्रश्न
Find the roots of the quadratic equation by using the quadratic formula in the following:
–x2 + 7x – 10 = 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 = `(-7 +- sqrt((-7)^2 - 4(-1)(-10)))/(2(-1))`
= `(-7 +- sqrt(9))/(-2)`
= `(7 +- 3)/2`
= 5, 2
APPEARS IN
संबंधित प्रश्न
Solve the equation by using the formula method. 3y2 +7y + 4 = 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 value of k for which the equation x2 + k(2x + k − 1) + 2 = 0 has real and equal roots.
Find the values of k for which the roots are real and equal in each of the following equation:
4x2 - 2(k + 1)x + (k + 4) = 0
For what value of k, (4 - k)x2 + (2k + 4)x + (8k + 1) = 0, is a perfect square.
Find the value(s) of k so that the quadratic equation 3x2 − 2kx + 12 = 0 has equal roots ?
Find the value of the discriminant in the following quadratic equation:
x2 +2x-2=0
Solve the following quadratic equation using formula method only
`2"x"^2- 2 sqrt 6 + 3 = 0`
In each of the following determine the; value of k for which the given value is a solution of the equation:
kx2 + 2x - 3 = 0; x = 2
Find the discriminant of the following equations and hence find the nature of roots: 3x2 – 5x – 2 = 0
Find the value(s) of k for which each of the following quadratic equation has equal roots: 3kx2 = 4(kx – 1)
The sum of the roots of the quadratic equation 3x2 – 9x + 5 = 0 is:
Mohan and Sohan solve an equation. In solving Mohan commits a mistake in constant term and finds the roots 8 and 2. Sohan commits a mistake in the coefficient of x. The correct roots are:
(x2 + 1)2 – x2 = 0 has:
State whether the following quadratic equation have two distinct real roots. Justify your answer.
`(x - sqrt(2))^2 - 2(x + 1) = 0`
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.
Find the nature of the roots of the quadratic equation:
4x2 – 5x – 1 = 0
Find the value(s) of 'a' for which the quadratic equation x2 – ax + 1 = 0 has real and equal 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 ______.
If the roots of x2 – px + 4 = 0 are equal, the value (values) of p is ______.
