CBSE Maths · Class 10
Chapter 4: Quadratic Equations
Name: ________________________
Date: ______________
Marks: ____ / 10
Standard form, factorisation, completing the square, quadratic formula, nature of roots and word problems.
Questions
- Solve x2−3x−10=0.
- Discuss nature of roots of 2x2−6x+3=0.
- Solve x+1/x=10/3.
- Find k so x2+2(k+1)x+k2=0 has equal roots.
- Solve 3x2+10x+73=0.
- Solve x2−5x=0.
- Product of two consecutive positive integers =306. Find them.
- Sum of squares of two consecutive odd positive integers =290. Find them.
- Roots of 2x2+x−4=0 by quadratic formula.
- A train travels 360 km at uniform speed. If speed had been 5 km/h more, it would have taken 1 h less. Find its speed.
Extra Practice (Optional)
- Solve 2x2−5x+32=0.
- Discriminant of 3x2−43x+4.
- Two-digit number problem: sum digits 9, product 18.
- Age problem quadratic form.
- Speed-time problem: boat's speed in still water.
Answer Key (For Teachers)
- Answer: 5,−2.
Working: Split: −3=−5+2; product −10. → (x−5)(x+2). - Answer: Two distinct real.
Working: D=36−24=12>0. - Answer: 3 or 1/3.
Working: 3x2−10x+3=0; factor (3x−1)(x−3). - Answer: k=−1/2.
Working: D=4(k+1)2−4k2=0; 2k+1=0. - Answer: −3,−7/3.
Working: Split middle: 10=7+3. → Factor as (3x+7)(x+3). - Answer: 0 or 5.
Working: x(x−5)=0. - Answer: 17,18.
Working: n(n+1)=306; n=17. - Answer: 11,13.
Working: (2n−1)2+(2n+1)2=290⇒8n2+2=290⇒n=6. - Answer: 4−1±33.
Working: x=4−1±1+32=4−1±33. - Answer: v=40 km/h.
Working: Let speed =v: v360−v+5360=1. → 360(v+5−v)=v(v+5)⇒v2+5v−1800=0⇒(v−40)(v+45)=0.
Gyaan Maths · CBSE Class 10 · Chapter 4