Advertisements
Advertisements
प्रश्न
Find the roots of the quadratic equation by using the quadratic formula in the following:
`x^2 + 2sqrt(2)x - 6 = 0`
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 = `(-2sqrt(2) +- sqrt((2sqrt(2))^2 - 4(1)(-6)))/(2(1))`
= `(-2sqrt(2) +- sqrt(32))/2`
= `(-2sqrt(2) +- 4sqrt(2))/2`
= `sqrt(2), -3sqrt(2)`
APPEARS IN
संबंधित प्रश्न
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.
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.
Determine the nature of the roots of the following quadratic equation:
2(a2 + b2)x2 + 2(a + b)x + 1 = 0
For what value of k, (4 - k)x2 + (2k + 4)x + (8k + 1) = 0, is a perfect square.
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 :
x2 +10x- 8= 0
Find the value of m for which the equation (m + 4)x2 + (m + 1)x + 1 = 0 has real and equal roots.
Solve for x: (x2 - 5x)2 - 7(x2 - 5x) + 6 = 0; x ∈ R.
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 ______.
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.
