CBSE Class 10 Mathematics Quadratic Equations Assignment Set 17

Question. Form a quadratic equation whose one root is \( (2+\sqrt{5}) \) and Sum of roots is 4.
Answer: \( x^2 - 4x - 1 = 0 \)

Question. Form a quadratic equation whose one root is \( \sqrt{7}+2 \) and product of roots is \( -3 \).
Answer: \( x^2 - 4x - 3 = 0 \)

Question. Form a quadratic equation whose roots are 3 and 5.
Answer: \( x^2 - 8x + 15 = 0 \)

Question. Form a quadratic equation whose sum of roots is 7 and product of roots is \( -3 \).
Answer: \( x^2 - 7x - 3 = 0 \)

Question. Find the discriminant of equation \( 2x^2 - x - 5 = 0 \).
Answer: 41

Question. Discuss the nature of roots of Equations
(i) \( 4x^2 + 4x - 1 = 0 \)
(ii) \( 9x^2 - 12x + 4 = 0 \)
(iii) \( 2x^2 - 4x + 7 = 0 \)
Answer:
(i) real but unequal
(ii) real but equal
(iii) Unreal

Question. For what value of \( k \), the equation \( 2x^2 + 3x + k = 0 \) have real and equal roots.
Answer: \( k = 9/8 \)

Question. Find \( K \) for equal roots
\( (K-12)x^2 + 2(K-12)x + 2 = 0 \)
Answer: \( K = 14 \)

Question. Find \( K \) for real roots from \( Kx^2 + 4x + 3 = 0 \)
Answer: \( K \le \frac{4}{3} \)

Question. Find \( K \) for not real roots from \( 2x^2 - 6x + K = 0 \)
Answer: \( K > \frac{9}{2} \)