What is a Quadratic Equation ? With Prctice set
Q. What is a Quadratic Equation ?
A quadratic equation is an equation of degree 2 (highest power of variable is 2).
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MCQs (Exam Practice)
Q1. Find the nature of roots of x2−4x+4=0. āĻĒā§ā§°āĻļā§āĻ¨: āĻ¸āĻŽāĻžāĻ§āĻžāĻ¨ā§° āĻĒā§ā§°āĻā§āĻ¤āĻŋ āĻāĻŋāĻ¨āĻžāĻā§āĻ¤ āĻā§°āĻ
Options: (a) Two distinct real roots (b) Equal real roots (c) No real roots (d) Imaginary
Ans: (b) Equal real roots
Explanation: D = b2−4ac = 16−16= 0 → equal roots. āĻŦā§āĻ¯āĻžāĻā§āĻ¯āĻž : D = 0 → āĻĻā§āĻāĻž āĻ¸āĻŽāĻžāĻ¨ āĻŦāĻžāĻ¸ā§āĻ¤ā§ą āĻ¸āĻŽāĻžāĻ§āĻžāĻ¨
Q2. Sum of roots of 2x2+3x−5=0 āĻĒā§ā§°āĻļā§āĻ¨: āĻŽā§āĻ˛āĻ¸āĻŽā§āĻšā§° āĻ¯ā§āĻāĻĢāĻ˛
Options: (a) −3/2 (b) 3/2 (c) 5/2 (d) −5/2
Ans: (a) −3/2
Explanation: Sum = −b/a = −3/2
Q3. Product of roots of x2−7x+10=0
Options: (a) 7 (b) 10 (c) -10 (d) -7
Ans: (b) 10
Explanation: Product = c/a = 10
Q4. If roots are equal, discriminant is:
Options: (a) > 0 (b) < 0 (c) = 0 (d) None
Ans: (c) = 0
Q5. Which is a quadratic equation ?
Options: (a) x3+2=0 (b) 2x2+3x=0 (c) x+5=0 (d) 1/x=2
Ans: (b) 2x2 + 3x = 0
Part 2: HOTS (Higher Order Thinking)
Q6. If one root of x2−5x+k=0 is 2, find k
Soln:
Put x = 2 → 4 − 10 + k = 0 → k = 6
Q7. Find k such that equation has equal roots:
x2 + kx + 9 = 0
b2 - 4ac = 0
Soln: k2 − 36 = 0 → k = ±6