The sum of the square of two consecutive natural numbers is 25. Represent this situation in the form of a quadratic equation.
x2 + (x + 1)2 = 25
x2 - (x + 1)2 = 25
(x + 1)2 - x2 = 25
x2 - (x + 1)2 + 25 = 0
Which of the following is a quadratic equation ?
x + 1/x + x3 = 0
x3 - 7x2 + 3x - 5 = 0
3x2 - 5x + 3 = x2 - x + 1
3x3 - 5x + 3 = x3 - x + 1
Find the value of the discriminant for the quadratic equation x2 + 4x - 21 = 0
99
98
100
101
Form a quadratic equation whose roots are 1 + √5 and 1 - √5.
x2 - 2x - 4 = 0
x2 + 2x + 4 = 0
x2 + 2x - 4 = 0
x2 - 2x + 4 = 0
If x2 + y2 = 25, xy = 12, then x =
{3, 4}
{3, -3}
{3, 4, -3, -4}
{-3, -3}
The equation 4x2 + 3x + 5 = 0 has
No real roots
Equal roots
Different roots
No roots
Two consecutive even integers are
x, x + 2
x, x + 1
x, x - 1
x, 2x
The standard form of a quadratic equation is
ax + b = 0, a ≠ 0
ax2 + bx + c = 0, a ≠ 0
ax3 + bx2 + cx + d = 0, a ≠ 0
ax4 + bx3 + c2 + dx + e = 0, a ≠ 0
A lotus is 2 m above the water in a pond. Due to wind the lotus slides on the side and only the stem completelysubmerges in the water at a distance of 10 m from the original position. Then the depth of water in the pond is
12 m
20 m
24 m
18 m
If α, β are the roots of x2 - 2px + q = 0 and γ, δ are roots of x2 - 2rx + s = 0 and α, β, γ, δ are in A.P then
p - q = r2 - s2
s - q = r2 - p2
r - s = p2 - q2
r - s = p - q