Advertisements
Advertisements
Question
Find whether the following equation have real roots. If real roots exist, find them.
`1/(2x - 3) + 1/(x - 5) = 1, x ≠ 3/2, 5`
Advertisements
Solution
Given equation is `1/(2x - 3) + 1/(x - 5) = 1, x ≠ 3/2, 5`
⇒ `(x - 5 + 2x - 3)/((2x - 5)(x - 5))` = 1
⇒ `(3x - 8)/(2x^2 - 5x - 10x + 25)` = 1
⇒ `(3x - 8)/(2x^2 - 15x + 25)` = 1
⇒ 3x – 8 = 2x2 – 15x + 25
⇒ 2x2 – 15x – 3x + 25 + 8 = 0
⇒ 2x2 – 18x + 33 = 0
On company with ax2 + bx + c = 0, we get
a = 2, b = – 18 and c = 33
∴ Discriminant, D = b2 – 4ac
= (–18)2 – 4 × 2(33)
= 324 – 264
= 60 > 0
Therefore, the equation 2x2 – 18x + 33 = 0 has two distinct real roots.
Roots, `x = (-b +- sqrt(D))/(2a)`
= `(-(-18) +- sqrt(60))/(2(2))`
= `(18 +- 2sqrt(15))/4`
= `(9 +- sqrt(15))/2`
= `(9 + sqrt(15))/2, (9 - sqrt(15))/2`
APPEARS IN
RELATED QUESTIONS
Solve the equation by using the formula method. 3y2 +7y + 4 = 0
Solve the quadratic equation 2x2 + ax − a2 = 0 for x.
Find the values of k for which the roots are real and equal in each of the following equation:
kx2 + kx + 1 = -4x2 - x
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 least positive value of k for which the equation x2 + kx + 4 = 0 has real roots.
Solve the following quadratic equation using formula method only
5x2 - 19x + 17 = 0
Solve the following quadratic equation using formula method only
3a2x2 +8abx + 4b2 = 0, a ≠ 0
For what values of k, the roots of the equation x2 + 4x +k = 0 are real?
`10x -(1)/x` = 3
Find the value of k for which the given equation has real roots:
9x2 + 3kx + 4 = 0.
Without solving the following quadratic equation, find the value of 'm' for which the given equation has real and equal roots.
x2 + 2(m – 1)x + (m + 5) = 0
The quadratic equation whose roots are 1:
The quadratic equation whose one rational root is `3 + sqrt2` is
If the equation x2 – (2 + m)x + (–m2 – 4m – 4) = 0 has coincident roots, then:
The roots of quadratic equation 5x2 – 4x + 5 = 0 are:
Which constant must be added and subtracted to solve the quadratic equation `9x^2 + 3/4x - sqrt(2) = 0` by the method of completing the square?
Which of the following equations has two distinct real roots?
Every quadratic equation has at least one real root.
If one root of the quadratic equation x2 + 12x – k = 0 is thrice the other root, then find the value of k.
One root of equation 3x2 – mx + 4 = 0 is 1, the value of m is ______.
