Advertisements
Advertisements
प्रश्न
Find the roots of the quadratic equation by using the quadratic formula in the following:
`x^2 - 3sqrt(5)x + 10 = 0`
Advertisements
उत्तर
The quadratic formula for finding the roots of quadratic equation
ax2 + bx + c = 0, a ≠ 0 is given by,
x = `(-b +- sqrt(b^2 - 4ac))/(2a)`
∴ x = `(-(-3sqrt(5)) +- sqrt((-3sqrt(5))^2 - 4(1)(10)))/(2(1))`
= `(3sqrt(5) +- sqrt(5))/2`
= `2sqrt(5), sqrt(5)`
APPEARS IN
संबंधित प्रश्न
Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.
Find the values of k for which the roots are real and equal in each of the following equation:
kx2 + 4x + 1 = 0
Find the values of k for which the roots are real and equal in each of the following equation:
9x2 - 24x + k = 0
If p, q are real and p ≠ q, then show that the roots of the equation (p − q) x2 + 5(p + q) x− 2(p − q) = 0 are real and unequal.
Write the value of k for which the quadratic equation x2 − kx + 4 = 0 has equal roots.
Solve the following quadratic equation using formula method only
3a2x2 +8abx + 4b2 = 0, a ≠ 0
Find the value of k for which the roots of the equation 3x2 -10x +k = 0 are reciprocal of each other.
Find the value(s) of k for which the pair of equations
kx + 2y = 3
3x + 6y = 10 has a unique solution.
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
3x2 + 2x - 1 = 0
Without actually determining the roots comment upon the nature of the roots of each of the following equations:
9a2b2x2 - 48abc + 64c2d2 = 0, a ≠ 0, b ≠ 0
Determine whether the given quadratic equations have equal roots and if so, find the roots:
3x2 - 6x + 5 = 0
Find the values of k so that the quadratic equation (4 – k) x2 + 2 (k + 2) x + (8k + 1) = 0 has equal roots.
Mohan and Sohan solve an equation. In solving Mohan commits a mistake in constant term and finds the roots 8 and 2. Sohan commits a mistake in the coefficient of x. The correct roots are:
The roots of the quadratic equation `1/("a" + "b" + "x") = 1/"a" + 1/"b" + 1/"x"`, a + b ≠ 0 is:
If the equation x2 – (2 + m)x + (–m2 – 4m – 4) = 0 has coincident roots, then:
Which of the following equations has the sum of its roots as 3?
Solve the equation: 3x2 – 8x – 1 = 0 for x.
Find the value(s) of 'a' for which the quadratic equation x2 – ax + 1 = 0 has real and equal roots.
If α and β be the roots of the equation x2 – 2x + 2 = 0, then the least value of n for which `(α/β)^n` = 1 is ______.
Equation 2x2 – 3x + 1 = 0 has ______.
