Advertisements
Advertisements
प्रश्न
Form the quadratic equation whose roots are:
`2 + sqrt(5) and 2 - sqrt(5)`.
Advertisements
उत्तर
Let a, β be the given roots.
Then a = `2 + sqrt(5) and beta = 2 - sqrt(5)`
a + β = `2 + sqrt(5) + 2 - sqrt(5) = 4`
and aβ = `(2 + sqrt(5)) (2 - sqrt(5))`
⇒ a + β = 4 and aβ = (2)2 - `(sqrt(5))^2`
⇒ a + β = 4 and aβ = 4 - 5
⇒ a + β = 4 and aβ = -1
Required quadratic equation
x2 - (a + β)x + aβ = 0
⇒ x2 - 4x - 1 = 0.
संबंधित प्रश्न
Solve the equation by using the formula method. 3y2 +7y + 4 = 0
Find the nature of the roots of the following quadratic equation. If the real roots exist, find them:
`3x^2 - 4sqrt3x + 4 = 0`
Find the values of k for which the roots are real and equal in each of the following equation:
x2 - 4kx + k = 0
Prove that both the roots of the equation (x - a)(x - b) +(x - b)(x - c)+ (x - c)(x - a) = 0 are real but they are equal only when a = b = c.
Given that one root of the quadratic equation ax2 + bx + c = 0 is three times the other, show that 3b2 – 16ac.
Choose the correct answer from the given four options :
If the equation 2x² – 5x + (k + 3) = 0 has equal roots then the value of k is
Choose the correct answer from the given four options :
Which of the following equations has two distinct real roots?
Find the value(s) of k for which each of the following quadratic equation has equal roots: (k + 4)x2 + (k + 1)x + 1 =0 Also, find the roots for that value (s) of k in each case.
If one root of the quadratic equation 3x2 – 8x – (2k + 1) = 0 is seven times the other, then find the value of k.
The nature of roots of the quadratic equation 9x2 – 6x – 2 = 0 is ______.
