Advertisements
Advertisements
प्रश्न
`10x -(1)/x` = 3
Advertisements
उत्तर
`10x -(1)/x` = 3
⇒ `(10x^2 - 1)/x` = 3
⇒ 10x2 - 3x -1 = 0
⇒ 10x2 - 5x + 2x - 1 = 0
⇒ 5x(2x - 1) + 1(2x - 1) = 0
⇒ (2x - 1)(5x + 1) = 0
⇒ 2x - 1 = 0 or 5x + 1 = 0
x = `(1)/(2)` or x = `- (1)/(5)` are two roots of the equation.
संबंधित प्रश्न
Is it possible to design a rectangular mango grove whose length is twice its breadth, and the area is 800 m2? If so, find its length and breadth.
If one root of the quadratic equation is `3 – 2sqrt5` , then write another root of the equation.
Find the values of k for which the roots are real and equal in each of the following equation:
5x2 - 4x + 2 + k(4x2 - 2x - 1) = 0
Find the roots of the equation .`1/(2x-3)+1/(x+5)=1,x≠3/2,5`
If `sqrt(2)` is a root of the equation `"k"x^2 + sqrt(2x) - 4` = 0, find the value of k.
Discuss the nature of the roots of the following equation: 3x2 – 7x + 8 = 0
If the roots of the given quadratic equation are real and equal, then find the value of ‘m’.
(m – 12)x2 + 2(m – 12)x + 2 = 0
(x2 + 1)2 – x2 = 0 has ______.
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 3x2 – 8x – (2k + 1) = 0 is seven times the other, then find the value of k.
