Advertisements
Advertisements
Question
Solve the following quadratic equation by using formula method: 5m2 + 5m – 1 = 0
Advertisements
Solution
Given quadratic equation is 5m2 + 5m – 1 = 0
Comparing with general form ax2 + bx + c = 0, we have
a = 5, b = 5 and c = –1
∴`X=(-b+-sqrt(b^2-4ac))/(2a`
`=(-5+-sqrt(5^2-4(5)(-1)))/(2*5)`
`=(-5+-sqrt(25+20))/10`
`=(-5+-sqrt45)/10`
`=(-5+-3sqrt5)/10`
∴`(-5+3sqrt5)/10`and `(-5-3sqrt5)/10`are the roots of the given equation.
RELATED QUESTIONS
If x=−`1/2`, is a solution of the quadratic equation 3x2+2kx−3=0, find the value of k
Without solving, examine the nature of roots of the equation 4x2 – 4x + 1 = 0
Find the values of k for which the roots are real and equal in each of the following equation:
4x2 - 3kx + 1 = 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
Solve the following quadratic equation using formula method only
4x2 + 12x + 9 = 0
Solve the following quadratic equation using formula method only
15x2 - 28 = x
Find the value of m for which the equation (m + 4)x2 + (m + 1)x + 1 = 0 has real and equal roots.
Solve for x : `9^(x + 2) -6.3^(x + 1) + 1 = 0`.
In each of the following, determine whether the given numbers are roots of the given equations or not; x2 – 5x + 6 = 0; 2, – 3
Find the value (s) of k for which each of the following quadratic equation has equal roots : (k – 4) x2 + 2(k – 4) x + 4 = 0
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
Find the values of m so that the quadratic equation 3x2 – 5x – 2m = 0 has two distinct real roots.
If the roots of px2 + qx + 2 = 0 are reciprocal of each other, then:
The roots of quadratic equation 5x2 – 4x + 5 = 0 are:
State whether the following quadratic equation have two distinct real roots. Justify your answer.
3x2 – 4x + 1 = 0
A quadratic equation with integral coefficient has integral roots. Justify your answer.
Find whether the following equation have real roots. If real roots exist, find them.
8x2 + 2x – 3 = 0
State whether the following quadratic equation have two distinct real roots. Justify your answer.
(x – 1)(x + 2) + 2 = 0
If one root of the quadratic equation x2 + 12x – k = 0 is thrice the other root, then find the value of k.
Which of the following equations has imaginary roots?
