8/4/2019 DPP2-Number System and Quadratic Equation 2

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Daily Practice Problems No-2(IIT JEE 2013 VCC)

MATHEMATICS Top ic : N um ber Sy ste m & Qua dr at ic Eq uat ion s D at e:

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Common Roots

1. Let , be the roots of equation x2 px + q = 0 and

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be the roots of equation x2 qx + r = 0, then value of r is.

(a )2

( )(2 )9

p q q p (b)2

( )(2 )9

q p p q (c)2

( 2 )(2 )9

q p q p (c)2

(2 )(2 )9

p q q p

2. If , , be the roots of the equation x(1 + x2) + x2(6 + x) + 2 = 0, then the value of 1 + 1 + 1 is

(a ) 3 ( b)12

(c)12

(d ) none of these

3. If the roots of x3 12 x2 + 39 x 28 = 0 are in A.P. then their common difference is

(a ) 1 ( b) 2 ( c) 3 ( d ) 4

4. The number of real roots of ( x + 3) 4 + ( x + 5) 4 = 16 is

(a ) 0 ( b) 2 ( c) 4 ( d ) none of these

5. If , ( < ) , are the roots of the equation x2 + b x + c = 0, where C < 0 < b, then

(a ) 0 < < (b) < 0 < < | | (c) < < 0 (d ) < 0 < | | <

Quadratic Expression and Its Graph

6. The roots of ax2

+ bx + c = 0, where a 0 and coefficients are real, are non-real complex and a + c < b. Then(a ) 4 a + c > 2 b (b) 4 a + c < 2 b (c) 4 a + c = 2 b (d ) none of these

7. If a > 1, roots of the equation (1 a ) x2 + 3 ax 1 = 0 are

(a ) one positive and one negative ( b) both negative

(c) both positive ( d ) both normal complex

8. If X denotes the set of real numbers p for which the equation x2 = p( x + p ) has its roots greater than p , then X is equalto

(a) 12, 2 (b) 1 1,2 4 (c) null set (d ) ( , 0)

9. If value of a for which the quadratic equation 3 x2 + 2( a 2 + 1) x+ (a 2 3 a + 2) = 0 possesses roots of opposite sign lies in

(a ) ( , 1) ( b) ( , 0) ( c) (1, 2) ( d )3

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10. If p > 2 and p N, then the equation x3 px + 1 = 0 cannot have

(a ) rational roots ( b) integral roots ( c) irrational roots ( d ) none of these