Advertisements
Advertisements
प्रश्न
`(2)/x^2 - (5)/x + 2` = 0
Advertisements
उत्तर
`(2)/x^2 - (5)/x + 2` = 0
⇒ `(2 - 5x + 2x^2)/x^2` = 0
⇒ 2x2 - 5x + 2 = 0
⇒ 2x2 - 4x - x + 2 = 0
⇒ 2x(x - 2) -1(x -2) = 0
⇒ (x - 2)(2x - 1) = 0
⇒ x - 2 = 0 or 2x - 1 = 0
⇒ x = 2 or x = `(1)/(2)` are two root of the equation.
संबंधित प्रश्न
Determine the nature of the roots of the following quadratic equation:
(x - 2a)(x - 2b) = 4ab
From the quadratic equation if the roots are 6 and 7.
Determine whether the given quadratic equations have equal roots and if so, find the roots:
`(4)/(3)x^2 - 2x + (3)/(4) = 0`
Find the values of k for which each of the following quadratic equation has equal roots: 9x2 + kx + 1 = 0 Also, find the roots for those values of k in each case.
Find the value(s) of k for which each of the following quadratic equation has equal roots: 3kx2 = 4(kx – 1)
If roots of a quadratic equation 3y2 + ky + 12 = 0 are real and equal, then find the value of ‘k’
If the roots of equation 3x2 + 2x + (p + 2) (p – 1) = 0 are of opposite sign then which of the following cannot be the value of p?
The probability of selecting integers a ∈ [–5, 30] such that x2 + 2(a + 4)x – 5a + 64 > 0, for all x ∈ R, 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.
Statement A (Assertion): If 5 + `sqrt(7)` is a root of a quadratic equation with rational co-efficients, then its other root is 5 – `sqrt(7)`.
Statement R (Reason): Surd roots of a quadratic equation with rational co-efficients occur in conjugate pairs.
