Q1.Nature of RootsEasy · 1m
What does the discriminant D = b² − 4ac tell us about the roots?
Answer: D>0: two distinct real roots; D=0: two equal real roots; D<0: no real roots.
Class 10 · Maths · Important Questions
Quadratic Equations — Important Questions
Q2.FactorisationMedium · 2m
Solve x² − 5x + 6 = 0 by factorisation.
Answer: (x−2)(x−3)=0 ⇒ x = 2 or x = 3.
Q3.Quadratic FormulaEasy · 2m
Write the quadratic formula for ax² + bx + c = 0.
Answer: x = (−b ± √(b² − 4ac)) / 2a.
Q4.Equal RootsMedium · 3m
Find k if x² − kx + 9 = 0 has equal roots.
Answer: D=0 ⇒ k² − 36 = 0 ⇒ k = ±6.
Q5.Word ProblemHard · 5m
The product of two consecutive positive integers is 306. Form and solve the equation.
Answer: x(x+1)=306 ⇒ x²+x−306=0 ⇒ (x−17)(x+18)=0 ⇒ x = 17, integers 17 and 18.
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