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Quadratic Equations Practice 1: Standard Form and Factorisation

Section A: Concept Check

Question 1mcq
Which of the following is a quadratic equation?
A.x2−5x+6=0x^2-5x+6=0
B.3x+7=03x+7=0
C.x3+x=0x^3+x=0
D.1x+2=0\frac{1}{x}+2=0
Question 2mcq
For which value of kk is (k−2)x2+3x+1=0(k-2)x^2+3x+1=0 not a quadratic equation?
A.22
B.00
C.11
D.−2-2
Question 3mcq
Convert x(x+3)=10x(x+3)=10 into standard form.
A.x2+3x−10=0x^2+3x-10=0
B.x2+3x+10=0x^2+3x+10=0
C.x2−3x−10=0x^2-3x-10=0
D.x2+10x+3=0x^2+10x+3=0
Question 4mcq
What is the standard form of (x−2)2=9(x-2)^2=9?
A.x2−4x−5=0x^2-4x-5=0
B.x2−4x+13=0x^2-4x+13=0
C.x2+4x−5=0x^2+4x-5=0
D.x2−2x−9=0x^2-2x-9=0
Question 5mcq
Solve x2−7x+12=0x^2-7x+12=0 by factorisation.
A.x=3,4x=3,4
B.x=−3,−4x=-3,-4
C.x=1,12x=1,12
D.x=7,12x=7,12

Section B: Factor and Solve

Question 6mcq
Solve 2x2−5x−3=02x^2-5x-3=0.
A.x=3,−12x=3, -\frac{1}{2}
B.x=−3,12x=-3, \frac{1}{2}
C.x=2,−3x=2, -3
D.x=32,−1x=\frac{3}{2}, -1
Question 7mcq
Solve 3x2−12x=03x^2-12x=0.
A.x=0,4x=0,4
B.x=4x=4
C.x=0,−4x=0,-4
D.x=3,4x=3,4
Question 8mcq
A student solves 5x2=20x5x^2=20x by dividing both sides by xx and gets only x=4x=4. What root was lost?
A.x=0x=0
B.x=1x=1
C.x=−4x=-4
D.x=5x=5
Question 9mcq
Which factorisation is correct for x2+x−12x^2+x-12?
A.(x+4)(x−3)(x+4)(x-3)
B.(x−4)(x+3)(x-4)(x+3)
C.(x+6)(x−2)(x+6)(x-2)
D.(x−6)(x+2)(x-6)(x+2)
Question 10mcq
A rectangle has length x+5x+5 and breadth x−2x-2, and area 4040. Which quadratic equation represents this?
A.x2+3x−50=0x^2+3x-50=0
B.x2+3x+40=0x^2+3x+40=0
C.x2−7x−40=0x^2-7x-40=0
D.x2+7x−50=0x^2+7x-50=0