Q41.If the equation x2 + ax + b = 0 has roots α and β, then value of (1 + α + α2) (1 + β + β2) is-
Correct answer: a2 + b2 – ab – a –b + 1
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Q42.The roots of the quadratic equation are real and equal if the discriminant is _____ zero.
Correct answer: =
Q43.One non zero root of the equation (((()))) 2 x 3x 2 2 8 =
Correct answer: 6
Q44.One solution of the quadratic equation 2 2x 7x 39 is
Correct answer: –3
Q45.Minimum possible number of real roots of a quadratic equation is
Correct answer: 0
Q46.What is the maximum number of distinct roots a quadratic equation can have?
Correct answer: 2
Q47.How many distinct real roots are there for the equation x2 -6x+5=0?
Correct answer: 2
Correct answer: [-4,4]
Q49.Maximum value of the expression 2 5 + 4x – 4x is
Correct answer: 6
Q50.If the roots of a quadratic equation ax2 +bx+6=0 are -3 and -2, then the value of 'b' is
Correct answer: 5
Q51.If the ratio of roots of an equation x2 - px + q = 0 is 1: 2, then the relation between p and q is
Correct answer: 2p2 = 9q
Q52.If 4 be the root of the equation x2 + ax – – – 12 = 0, then another root is
Correct answer: –3
Q53.If b = c = 0 in the equation ax2 + bx + c = 0, then the value of roots are
Correct answer: 0, 0
Q54.What is the nature of the roots of this equation 2 x – 2 7x – 2 = 0?
Correct answer: Real, Unequal, Irrational
Correct answer: Rational, Real
Correct answer: b = 0
Q57.What is the addition of two roots of the equation 3x2 - 5x + 7 = 0?
Correct answer: 5/3
Q58.Which of the following equations is having the roots 2 and (-3)?
Correct answer: x2 + x - 6 = 0
Q59.If the subtraction of two roots is 2, of the equation 2x2 - 12x + m + 2 = 0, then the value of m is
Correct answer: m = 14
Q60.If one root of any equation is (2 – 3i) (where i = –1), then what is the equation?
Correct answer: x2 - 4x + 13 = 0