Quadratic Equation Quick Revision/Summary| ICSE/CBSE | Mathematics | Class 9 and 10

QUADRATIC EQUATIONS


TYPE I – NATURE OF ROOTS
Question 1
Find the value of k for which the quadratic equation x 2 + 4kx + (k2 – k + 2) = 0
has real and equal roots
Question 2
Find the value of p for which the quadratic equation
(2p + 1)x2 – (7p + 2)x + (7p – 3) = 0 has real and equal roots


TYPE II – SOLVING BY FACTORIZATION METHOD
Question 3
(i) x2 – 3x – 10 = 0 (ii) 6p2 + 11p – 10 = 0 (iii) 2x2 – 8x – 24 = 0. x ϵ N
TYPE III – SOLVING BY FORMULA METHOD – ONE DECIMAL, TWO
DECIMAL, THREE DECIMAL PLACES
Question 4
Solve the following quadratic equations using formula and give your answer
correct to one, two and three decimal places
(i) x2 – 3(x + 3) = 0 (ii) 3x2 – x – 7 = 0


TYPE IV – SOLVING BY FORMULA METHOD – ONE SIGNIFICANT,
TWO SIGNIFICANT, THREE SIGNIFICANT PLACES
Question 5
Solve the following quadratic equations using formula and give your answer
correct to one, two and three significant places
(i) 5x2 – 3x – 3 = 0 (ii) 4x2 + 4x – 10 = 0


TYPE V – DIRECT EQUATIONS
1 1 1
(i) + + =0
𝑥−2 𝑥−3 𝑥−4
2𝑥−1 𝑥+3 1
(ii) 2( ) − 3 (2𝑥−1) = 5, 𝑥 ≠ −3, 2
𝑥+3