ECAT Mathematics Chapter 6 Quadratic Equations Online Test With Answers

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ECAT Mathematics Chapter 6 Quadratic Equations Online Test

Sr. # Questions Answers Choice
1 Another name of quadratic equation is Polynomial 2nd degree polynomial Linear equation simaltaneous equations
2 A quadratic equation in x is an equation that can be witten in the form ax<sup>2 </sup>+ b = 0 ax<sup>3</sup> +b<sup>2</sup>+c=0 ax<sup>2</sup> +bx+c=0 ax<sup>3</sup> +bx<sup>3</sup>+cx=0
3 If a (p + q)2+ bpq +c = 0 and a (p + r)2+ 2 bpr + c = 0, then qr equals p<sup>2</sup>+ c/a p<sup>2</sup>+ a/c p<sup>2</sup>+ c/a p<sup>2</sup>- c/a
4 If sinαand cosαare the roots of the equation px2+ qx + r =0, then p<sup>2</sup>- q<sup>2</sup>+ 2pr = 0 (p + r)<sup>2</sup>= q<sup>2</sup>- r<sup>2</sup> p<sup>2</sup>+ q<sup>2</sup>- 2pr = 0 (p - r)<sup>2</sup>= q<sup>2</sup>+ r<sup>2</sup>
5 Root of the equation 3x-1+ 31-x= is 2 1 0 -1
6 For the equation |x2| + |x| -6 =0, the roots are One and only one real number Real with sum one Real with sum zero Real with product zero
7 Lies between 4 and 7 Lies between 5 and 9 Has no value between 4 and 7 Has no value between 5 and 9
8
9 15 9 7 8
10 If the roots of ax2+ bx + c = 0 (a > 0) be greater than unity, then a + b + c = 0 a + b + c &gt; 0 a + b + c &lt; 0 None of these
11 Ifα,βare the roots of ax2+ bx + c = 0 andα+ h,β+ h are the roots of px2+ qx + r=0, then h =
12 If the roots of ax2- bx - c = 0 change by the same quantity, then the expression in a, b, c that does not change is
13 Let the equation ax2- bx + c = 0 have distinct real roots both lying in the open interval (0, 1) where a, b, c are given to be positive integers. Then the value of the ordered triplet (a, b, c) can be (5, 3, 1) (4, 3, 2) (5, 5, 1) (6, 4, 1)
14 Two real roots Two positive roots Two negative roots One positive and one negative root
15 In a quadratic equation with leading co-efficient 1, a student reads the co-obtain the roots as - 15 and -4. The correct roots are 6, 10 -6, -10 8, 8 -8, -8
16 (-1, 2) (-1, 1) (1, 2) {-1}
17 1 2 0 4
18 If the roots of x2+ ax + b = 0 are non-real, then for all real x, x2+ ax + b is Negative Positive Zero Nothing can be said
19 The equation (cos p - 1)x2+ x (cos p) + sin p = 0 in the variable x, has real roots, then p can take any value in the interval (0, 2<span style="color: rgb(34, 34, 34); font-family: &quot;Times New Roman&quot;; font-size: 24px; text-align: center; background-color: rgb(255, 255, 224);"><i>π</i></span>) (-<span style="color: rgb(34, 34, 34); font-family: &quot;Times New Roman&quot;; font-size: 24px; text-align: center; background-color: rgb(255, 255, 224);"><i>π</i></span>, -0) (0,<span style="color: rgb(34, 34, 34); font-family: &quot;Times New Roman&quot;; font-size: 24px; text-align: center; background-color: rgb(255, 255, 224);"><i>π</i></span>) None of these
20 If 2x1/3+ 2x-1/3= 5, then x is equal to 1 or -1 2 or 1/2 8 or 1/8 4 or 1/4
21 Rational Irrational Non-real Zero
22 Only one real solution Exactly three real solution Exactly one rational solution Non-real roots
23 The value of k (k > 0) for which the equation x2+ kx + 64 = 0 and x2- 8x + k = 0 both will have real roots is 8 -16 -64 16
24 The set of real roots of the equation log(5x + 4)(2x +3)3- log(2x + 3)(10x2+ 23x + 12) = 1 is {-1} {-3/5} Empty set {-1/3}
25 (a - c)<sup>2</sup>= b<sup>2</sup>- c<sup>2</sup> (a - c)<sup>2</sup>= b<sup>2</sup>+ c<sup>2</sup> (a + c)<sup>2</sup>= b<sup>2</sup>- c<sup>2</sup> (a + c)<sup>2</sup>= b<sup>2</sup>+ c<sup>2</sup>
26 If x2 + px + 1 is a factor of ax3+ bx +c, then a<sup>2</sup>+ c<sup>2</sup>= -ab a<sup>2</sup>- c<sup>2</sup>= -ab a<sup>2</sup>- c<sup>2</sup>= ab None of these
27 n if n is even 0 for any natural number n 1 if in odd None of these
28 The roots of the equation 22x- 10.2x+ 16 = 0 are 2, 8 1, 3 1, 8 2, 3
29
30 The value of p for which both the roots of the equation 4x2- 20x + (25p2+ 15 p - 66) = 0 are less than 2, lies in
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