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WorksheetsMBA Factors CH 15 LD 2.3
Total questions: 25
Worksheet time: 50mins
If α, β are the roots of the quadratic equation x2 + mx + 1 = 0 and γ, δ are the roots of the equation x2 + nx + 1 = 0, then the value of (α − γ) (β − γ) (α + δ )(β + δ ) is equal to
n2 − m2.
m2 − n2 .
2 m2 − n2 .
Find the roots of the quadratic equation bx2 − 2ax + a = 0
b±a−bb
b±a−ba
a±a−ba
a± a+ba
If x2 + 3x − 10 is a factor of 3x4 + 2x3 − ax2 + bx − a + b − 4, then the closest approximate values of a and b are
If x is real, the smallest value of the expression 3x2 − 4x + 7 is:
2/3
7/9
The number of possible real solution(s) of y in the equation y2 − 2y cos x + 1 = 0 is____?
A polynomial ax3 + bx2 + cx + d intersects the x−axis at 1 and −1, and y-axis at 2. The value of b is:
If x3 − mx2 + nx − p = 0 has three roots α, β, γ. If we add 3 in each of the roots of x3 − mx2 + nx − p = 0 then we get the roots of the equation x3 − ax2 + bx − 27 = 0. What is the value of p + 9m + 3n.
If the roots of the equation x3 + qx2 + rx + s = 0 are in GP, then which of the following is true:
r 2 = q2 s
r 3 = q3 s
r = qs2
r = qs3
The graph of ax2 + bx + c is shown below. Then which of the following is true?
If ‘x’ is a real number then what is the number of solutions for the equation: (x8 + 12)1/2 = x4 − 2
How many integer values of ‘p’ are there such that the inequality x2 + 4px + (p + 3) > 0 is true for all values of x?
(a)
If g (x)=x3−px2−2qx−r can be factorized as (x − p) (x − q) (x − r), then f(4) = ?
(a)
The roots of x3 − px2 + qx − r = 0 are a, b, c while the roots of x3 + wx2 + yz − 47 = 0 are a + 2, b + 2, c + 2, Then the value of 4p + 2q + r=?
(a)
One of the roots of the equation x2 + bx + 3b = 0 (b ∈ R) is thrice the other root, What is the value of 3b.
(a)
One of the roots of the equation x2 + bx + 3b = 0 (b ∈ R) is thrice the other root, Which of the following options correctly represents roots of the equation x2 − 33x + 17b = 0
The roots of x2 + 5x + a = 0 are p and q while the roots of x2 + 23x + b = 0 are q and r. If p, q, r are in an Arithmetic Progression then the value of |a × b| = ?
(a)
f (x) = (x − 2)(x2 + 2x + 5)
If a, b, c are the roots of f(x) = 0, then the value of a3 + b3 + c3 would be equal to?
(a)
If f(x) = px2 + qx + r and f(x) is exactly divisible by (x + 2) and (x + 3) but leaves remainder of 7 when divided by (x − 1), find the approximate value of q?
(a)
If f (x)=4x−7 x , which of the following statements is true about the roots of the equation f(x) = 2.
If the equation ax2 + bx + a = 0(a > 0) has real and positive roots then which of the following is always true?
If f(x) = px2 + qx + r and g(x) = rx2 + qx + p. If one root of f(x) = 0 is 2 and one root of g(x) = 0 is ¼, then find the sum of the roots of f(x) and g(x).
(a)
The number of distinct points at which the curve y3 − 4y2 + x2 − 5x + 3y = 0 intersects either the y-axis or the x-axis is.
(a)
If the sum of the roots of the quadratic equation px2 + qx + r = 0 is equal to the sum of the square of their reciprocals, mark all the correct statements.
