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 the equation x2 + 4x + k has real and distinct roots, then
k = 4
k ≥ 4
k < 4
k ≤ 4
The roots of the quadratic equation x2 - 2x + 1 = 0 are
1, 1
1, -1
-1, -1
2, 2
If the sum of the squares of two consecutive positive even numbers is 340, then what is the sum of the two even numbers?
24
26
28
30
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
If the roots of the quadratic equation ax2 + bx + c are sin α and cos α, then
a2 + b2 = c2
a2 - 2bc = b2
b2 + 2ac = a2
b2 - 2ac = a2
Find the value of k of the quadratic equation 2x2 + kx + 3 = 0, so that it has equal roots.
± 2√3
± 2√6
± 2√7
± √2
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
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
Find the nature of the roots of the quadratic equation 2x2 - 6x + 3 = 0.
Two distinct real roots
Two equal real roots
No real roots
No roots
