M0IITU01 - Quadratic equations qns

M0IITU01 - Quadratic equations qns - QUADRATIC EQUATIONS 1...

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1 QUEST TUTORIALS Head Office : E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439 1. If one root of 5x 2 + 13x + k = 0 is reciprocal of the other, then k = (A) 0 (B) 5 (C) 6 1 (D) 6 2. If the roots of the equation, ax 2 + bx + c = 0 be α & β , then the roots of the equation cx 2 + bx + a = 0 are : - α , - β α , β 1 α 1 , β 1 None of these 3. If the roots of the given equation, (m 2 + 1) x 2 + 2 amx + a 2 - b 2 = 0 be equal, then : a 2 + b 2 (m 2 + 1) = 0 b 2 + a 2 (m 2 a 2 2 (m 2 b 2 - a 2 2 4. If P(x) = ax 2 + bx + c and Q(x) = - ax 2 + dx + c where ac 0, then P(x) . Q(x) = 0, has atleast : Four real roots Two real roots Four imaginary roots 5. If a root of the equation, 2 +bx+c=0 be reciprocal of a root of the equation, a x 2 + b x + c = 0 then : (cc - aa ) 2 = (ba - cb ) (ab - bc ) (bb - ) 2 = (ca - - ) - ) 2 + + ) None of these 6. If the difference of the roots of the equation, x 2 - bx + c = 0 be 1, then b 2 - 4c - 1 = 0 b 2 - 4c = 0 b 2 - 4c + 1 = 0 b 2 + 4c - 1 = 0 7. Let y = ( ) ( ) ( ) x x x + - - 1 3 2 , then all real values of x for which y takes real values are : - 1 x < 2 or x 3 x < 3 x > 2 1 3 None 8. 2 + i 3 is a root of the equation, x 2 + px + q = 0, where p & q are real, then (p, q) = (- 4, 7) (4, - 7) (4, 7) 9. (x + 1) is a factor of x 4 - (p - 3) x 2 - (3p - 5) x 2 + (2p - 7) x + 6, then p = 4 2 1 10. x = 2+2 2/3 +2 1/3 , then, x 3 -6x 2 +6x= 3 2 1 11. The co-efficient of x in the equation x 2 + px + q = 0 was taken as 17 in place of 13, its roots were found to be - 2 and - 15 . The roots of the original equation are : 3, 10 - 3, - 10 - 5, - 8 QUADRATIC EQUATIONS
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2 QUEST TUTORIALS Head Office : E-16/289, Sector-8, Rohini, New Delhi, Ph. 65395439 12. Let a, b, c be real numbers a 0 . If α is a root of a 2 x 2 + bx + c = 0, β is a root of a 2 x 2 - bx - c = 0 & 0 < α < β then the equation, a 2 x 2 + 2bx + 2c = 0 has a root γ that always satisfies : (A) γ = 2 β + α (B) γ α + 2 β (C) γ α (D) α γ β 13. If x 2 - 3x + 2 be a factor of x 4 - px 2 + q, then (p, q) = (3, 4) (4, 5) (4, 3) (5, 4) 14. If one root of the quadratic equation ax 2 + bx + c = 0 is equal to the n th
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M0IITU01 - Quadratic equations qns - QUADRATIC EQUATIONS 1...

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