Advertisements
Advertisements
प्रश्न
Solve the following quadratic equation by using formula method: 5m2 + 5m – 1 = 0
उत्तर
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.
संबंधित प्रश्न
Without solving, examine the nature of roots of the equation x2 – 5x – 2 = 0
Without solving, examine the nature of roots of the equation 4x2 – 4x + 1 = 0
Find the value of p, for which one root of the quadratic equation px2 – 14x + 8 = 0 is 6 times the other.
The 4th term of an A.P. is 22 and the 15th term is 66. Find the first terns and the common
difference. Hence find the sum of the series to 8 terms.
If 1 is a root of the quadratic equation 3x2 + ax – 2 = 0 and the quadratic equation a(x2 + 6x) – b = 0 has equal roots, find the value of b ?
What is the nature of roots of the quadratic equation 4x2 − 12x − 9 = 0?
Determine, if 3 is a root of the given equation
`sqrt(x^2 - 4x + 3) + sqrt(x^2 - 9) = sqrt(4x^2 - 14x + 16)`.
`10x -(1)/x` = 3
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.
If one root of the quadratic equation ax2 + bx + c = 0 is double the other, prove that 2b2 = 9 ac.
In each of the following, determine whether the given numbers are roots of the given equations or not; x2 – x + 1 = 0; 1, – 1
Find the discriminant of the following equations and hence find the nature of roots: 16x2 - 40x + 25 = 0
Find the value(s) of k for which each of the following quadratic equation has equal roots: 3kx2 = 4(kx – 1)
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:
The value of k for which the equation x2 + 2(k + 1)x + k2 = 0 has equal roots is:
Find the roots of the quadratic equation by using the quadratic formula in the following:
5x2 + 13x + 8 = 0
If the coefficient of x2 and the constant term have the same sign and if the coefficient of x term is zero, then the quadratic equation has no real roots.
The sum of all integral values of k(k ≠ 0) for which the equation `2/(x - 1), 1/(x - 2) = 2/k` in x has no real roots, is ______.
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 x2 + 12x – k = 0 is thrice the other root, then find the value of k.
