CBSE Class 10 Quadratic Equations Sure Shot Questions Set D

CBSE Class 10 Quadratic Equations Sure Shot Questions Set D. There are many more useful educational material which the students can download in pdf format and use them for studies. Study material like concept maps, important and sure shot question banks, quick to learn flash cards, flow charts, mind maps, teacher notes, important formulas, past examinations question bank, important concepts taught by teachers. Students can download these useful educational material free and use them to get better marks in examinations.  Also refer to other worksheets for the same chapter and other subjects too. Use them for better understanding of the subjects.

1. Find the value of k for which the quadratic equation 2x²+ kx + 3 = 0 has two real equal roots.

2. Find the value of k for which the quadratic equation kx(x – 3) + 9 = 0 has two real equal roots.

3. Find the value of k for which the quadratic equation 4x²– 3kx + 1 = 0 has two real equalroots..

4. If –4 is a root of the equation x²+ px – 4 = 0 and the equation x²+ px +q = 0 has equal roots, find the value of p and q.

5. If –5 is a root of the equation 2x²+ px – 15 = 0 and the equation p(x²+ x) +k = 0 has equal roots, find the value of k.

6. Find the value of k for which the quadratic equation (k – 12)x²+ 2(k – 12)x + 2 = 0 has two real equal roots..

7. Find the value of k for which the quadratic equation k²x²– 2(k – 1)x + 4 = 0 has two real equal roots..

8. If the roots of the equation (a – b)x²+ (b – c)x + (c – a) = 0 are equal, prove that b + c = 2a.

9. Prove that both the roots of the equation (x – a)(x – b) + (x – b)(x – c)+ (x – c)(x – a) = 0 arereal but they are equal only when a = b = c.

10. Find the positive value of k for which the equation x²+ kx +64 = 0 and x²– 8x +k = 0 will have real roots.

11. Find the value of k for which the quadratic equation kx²– 6x – 2 = 0 has two real roots.

12. Find the value of k for which the quadratic equation 3x² + 2x + k= 0 has two real roots.

13. Find the value of k for which the quadratic equation 2x²+ kx + 2 = 0 has two real roots.

14. Show that the equation 3x²+ 7x + 8 = 0 is not true for any real value of x.

15. Show that the equation 2(a²+ b²)x² + 2(a + b)x + 1 = 0 has no real roots, when a ¹ b.

16. Find the value of k for which the quadratic equation kx²+ 2x + 1 = 0 has two real and distinct roots.

17. Find the value of p for which the quadratic equation 2x²+ px + 8 = 0 has two real and distinct roots.

18. If the equation (1 + m²)x²+ 2mcx + (c²– a²) = 0 has equal roots, prove that c² = a²(1 + m²). 

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