Mathematics ECAT Pre Engineering Chapter 6 Quadratic Equations Online Test With Answers

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Mathematics ECAT Pre Engineering Chapter 6 Quadratic Equations Online Test

Sr. # Questions Answers Choice
1 The roots of (b-c)x2+(c-a) x+a-b=0 are equal if 2b = a+c 2a = b+c 2c = a+b a + b + c =0
2 The roots of ax2+bx+c=0 are Rational ⇔ b2 -4 ac ≥ 0 Irrational ⇔ b2-4 ac > 0 Real ⇔ b2-4 ac ≠ 0 Rational⇔ b2-4 ac = 0
3 If a,β are the roots of ax2+bx+c=0,the equation whose roots are doubled is ay2 +2by+c=0 ay2+2by+4c=0 ay2+2by+c=0 ay2+by+4c=0
4 If w+w2 is a root of (x+1)(x+2)(x+3)(x+4) = k, then k=0 k=1 k=w k=w2
5 (x +a)(x +b)(x +c)(x +) = k, k≠0 is reducible to quadratic form only if a+b=c+d a+c=b+d a+d=b+c All are correct
6 The value of x for which the polynomials x2 - 1 and x2 -2x + 1 vanish simultaneously is 2 1 -1 -2
7 The expression x2 - x + 1 has One proper linear factor No proper linear factor Two proper linear factors None of these
8 The condition for ax2 + bx c to be expressed as the product of linear polynomials is b4 - 4ac =0 b4- 4ac ≥0 b4- 4ac <0 b4= 4ac
9 If the equation x2+2x-3=0 and x2+3x-k=0 have a common root then the non - zero value of k is 1 3 2 4
10 Consider the equation px2 + qx + r = 0 where p,q,r are real The roots are equal in magnitude but opposite in sign when q = 0, r = 0,p ≠ 0 p = 0,qr≠ 0 r = 0,pq≠ 0 q = 0, pq≠ 0
11 If a,β are the roots of the equation x2 + kx +12 = 0 such that a - β = 1, the value of k is 0 ±1 ±5 ±7
12 The positive value of k for which the equation x2 + kx + 64 = 0 has one of the roots 0 4 64 8 All values of k
13 The sum of the roots of the equation x2 -6x +2 = 0 is -6 2 -2 6
14 The roots of ax2 + bx + c = 0 are always unequal if b2 - 4ac = 0 b2- 4ac ≠ 0 b2- 4ac > 0 b2- 4ac ≥ 0
15 A polynomial of arbitrary degree f(x) = o f(x) = x f(x) = a f(x) = ax + b,a ≠ 0
16 (1+w)(1+w2)(1+w4)(1+w8)....50 factors 0 -1 1 2
17 If x - 1 is a factor of x4 - 5x2 + 4 then other factor is (x + 2)2(x - 1) (x + 2)(x - 1)2 (x+2)(x2- x- 2) (x + 2)2(x - 1)2
18 The two parts into which 57 should be divided so that their product is 782 are 43,14 34,23 33,24 44,13
19 The roots of the equation 4x - 3.2x+2 + 32 = 0 would include 1 and 3 1 and 4 1 and 2 2 and 3
20 If one root of 5x2 + 13x + k = 0 be the reciprocal of the other root the value of k is 0 2 1 5
21 If a,βare the roots of the equation x2 - 8x + p = 0 and a2 + β2= 40,then value of p is 8 12 10 14
22 The solution of equation x2 + 2 = 0 in the set of real number is Infinite set Singleton set Null set None of these
23
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