Advertisements
Advertisements
Question
If one root of the quadratic equation is `3 – 2sqrt5` , then write another root of the equation.
Advertisements
Solution
One root of the quadratic equation is given to be `3 – 2sqrt5`
The other root will be the conjugate of `3 – 2sqrt5
conjugate of `3 – 2sqrt5=3 + 2sqrt5`
APPEARS IN
RELATED QUESTIONS
Find the value of k for which the equation x2 + k(2x + k − 1) + 2 = 0 has real and equal roots.
The 4th term of an A.P. is 22, and the 15th term is 66. Find the first term and the common difference. Hence, find the sum of the series to 8 terms.
Determine the nature of the roots of the following quadratic equation:
(x - 2a)(x - 2b) = 4ab
Find the values of k for which the roots are real and equal in each of the following equation:
`kx^2-2sqrt5x+4=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?
ax2 + (4a2 - 3b)x - 12 ab = 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
Find the value of k so that sum of the roots of the quadratic equation is equal to the product of the roots:
(k + 1)x2 + (2k + 1)x - 9 = 0, k + 1 ≠ 0.
If – 5 is a root of the quadratic equation 2x2 + px – 15 = 0 and the quadratic equation p(x2 + x) + k = 0 has equal roots, find the value of k.
Find the value(s) of m for which each of the following quadratic equation has real and equal roots: x2 + 2(m – 1) x + (m + 5) = 0
If the roots of ax2 + bx + c = 0 are in the ratio m : n, then:
The roots of the equation 7x2 + x – 1 = 0 are:
If p, q and r are rational numbers and p ≠ q ≠ r, then roots of the equation (p2 – q2)x2 – (q2 – r2)x + (r2 – p2) = 0 are:
State whether the following quadratic equation have two distinct real roots. Justify your answer.
`2x^2 - 6x + 9/2 = 0`
Let p be a prime number. The quadratic equation having its roots as factors of p is ______.
Find the nature of the roots of the quadratic equation:
4x2 – 5x – 1 = 0
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 ______.
The roots of the quadratic equation x2 – 6x – 7 = 0 are ______.
