Quadratic Equation 2013
Q1: Solve x2-5x+6 = 0
Q2: Solve 27x2-10x+1 = 0
Q3: Solve x2+4i x- 4 = 0
Q4: Solve x2-(7-i) x + (18-i) = 0.
Q5: Write an equation whose roots are 13, 89.
Q6: If α, β are roots of ax2+bx+c=0, find the value of 1/α+1/β; α2+β2
Q7: If α, β are roots of x2-a(x+1)-c=0, find the value of (1+α) (1+β)
Q8: If α, β are roots of ax2+bx+c=0, write the equation whose roots are 1/α4 and -1/β4.
Q9: If 3+√5 is a root of x2+bx+c=0, find the values of b and c, given that b and c are real.
Q10: The equation x2-kx+k+2=0 will have equal roots for what value(s) of k?
Q11: Find the number of real roots of the equation (x2+2x)2-(x+1)2-55=0.
Q12: Find the number of solutions of x2+|x-1|=1
Q13: Find the value of λ such that x2+2x+3λ=0 and 2x2+3x+5λ=0 have a non zero common root.
Q14: If α, β are roots of x2+p x+ 1 = 0 and γ, δ are the roots of x2+qx+1=0, evaluate:
(α- γ)(α+ δ)(β- γ)(β+ δ).
Q15: The real numbers x1, x2, x3 satisfying the equation x 3 -x2 + bx + c =0 are in AP. Find the
intervals in which b and c lie.
Q16: Find the equation whose roots are cube of the roots of the equation ax3+bx2+cx+d=0.
Q17: The number of roots of the equation
(𝑥+2)(𝑥−5)
(𝑥−3)(𝑥+6)
=
(𝑥−2)
(𝑥+4)
Q18: Solve 𝑥 = √2 + √2 + √2 + √2 + ⋯
(Ans: only one root)
(Ans: x=2 is only solution)
Q19: If a,b,c are the sides of the ▲ABC and equations 𝑎𝑥 2 + 𝑏𝑥 + 𝑐 = 0 and 5𝑥 2 + 12𝑥 + 13 = 0
have a common root then, find the value of ∟C.
(Ans=900)
Q20: The sum of all the values of ‘m’ for which the roots x1 and x2 of the quadratic equation
𝑥 2 − 2𝑚𝑥 + 𝑚 = 0 Satisfy the condition 𝑥13 + 𝑥23 = 𝑥12 + 𝑥22
(ans=5/4
Q21: If the roots of (𝑎 − 𝑏)𝑥 2 + (𝑏 − 𝑐)𝑥 + (𝑐 − 𝑎) = 0 are real and equal, then show that 2𝑎 = 𝑏 + 𝑐.
Q22: Show that expression 𝑥 2 + 2(𝑎 + 𝑏 + 𝑐)𝑥 + 3(𝑏𝑐 + 𝑐𝑎 + 𝑎𝑏) will be a perfect square if 𝑎 = 𝑏 = 𝑐 .
Q23:
Submitted by amit sir
class 11
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