1. If the product of the roots of the equation \(3x^2 - 5x + b = 0\) is \(4\), the value of \(b\) will be –
(a) \(\cfrac{5}{3}\) (b) \(\cfrac{3}{5}\) (c) 12 (d) -12
2. If the product of the roots of the equation \(x^2 - 3x + k = 10\) is \(-2\), then find the value of \(k\).
3. If the sum and product of the roots of the equation \(x^2 - x = k(2x - 1)\) are equal, what is the value of \(k\)?
4. If the product of the roots of the equation \(x^2 - 3x + k = 10\) is -2, then the value of \(k\) will be _____.
5. If the product of the roots of the equation \(3x^2 - 5x + b = 0\) is 4, then what is the value of \(b\)?
6. What is the value of \(k\) if the sum and product of the roots of the equation \(kx^2 + 2x + 3k = 0\) \((k \ne 0)\) are equal?
7. Find the ratio of the sum and product of the roots of the equation \(7x^2 - 12x + 18 = 0\).
8. If the product of the roots of the equation \(x^2 – 5x + k = 12\) is \(–3\), find the value of \(k\).
9. The ratio of the product and the sum of the roots of the equation \(ax^2 - bx + c = 0\) is – ____
10. If the equation \(ax^2 - 5x + c = 0\) has both the sum and product of its roots equal to \(10\), then which of the following is correct?
11. If the equation \(kx^2 + 6x + 4k = 0\) has equal values for the sum and product of its roots, then what is the value of \(k\)?
(a) \(-\cfrac{3}{2}\) (b) \(\cfrac{3}{2}\) (c) \(\cfrac{2}{3}\) (d) \(-\cfrac{2}{3}\)
12. If the sum of the roots of the equation \(x^2 - (k + 6)x + 2(2k - 1) = 0\) is half of their product, then what is the value of \(k\)?
(a) 6 (b) 7 (c) 1 (d) 5
13. If the product of the roots of the quadratic equation \(3x^2 – 4x + k = 0\) is 5, then what will be the value of \(k\)?
(a) 5 (b) -12 (c) 15 (d) -20
14. If the product of the roots of the equation \(x^2 - 3x + k = 10\) is \(-2\), determine the value of \(k\).
(a) -2 (b) -8 (c) 8 (d) 12
15. If the sum of the roots of the equation \(x^2 - x = k(2x - 1)\) is zero, determine the product of the roots.
16. If the product of the roots of the equation \(x^2 - 2x + k = 8\) is \(-2\), then the value of \(k\) is—
(a) -2 (b) 6 (c) 1 (d) -6
17. If the sum of the roots of a quadratic equation is 14 and their product is 24, form the quadratic equation.
18. What is the ratio of the sum and product of the roots of the equation \[ 7x^2 - 66x + 27 = 0? \]
19. If the product of the roots of the equation \(x^2 - 3x + k = 10\) is \(-2\), then the value of \(k\) is —
20. The ratio of the sum and the product of the roots of the equation \(7x^2 - 12x + 18 = 0\) is _________
21. If the sum of the roots of a quadratic equation is 14 and the product is 24, write the quadratic equation.
22. If the sum and the product of the roots of the equation \(kx^2 + 2x + 3k = 0\) \((k \ne 0)\) are equal, find the value of \(k\).
23. If the sum of the roots of the quadratic equation \(x^2 - px + q = 0\) is three times their product, then show that \(2p^2 = 9q\).
24. The roots of the equation \(ax^2+bx+c=0\) will be equal in magnitude but opposite in sign if-
(a) \(c=0, a≠0\) (b) \(b=0, a≠0\) (c) \(c=0, a=0\) (d) \(b=0, a=0\)
25. If the roots of the equation \( ax^2+bx+c=0 \,(a\ne 0) \) are real and equal, then
(a) \(c=\cfrac{-b}{2a}\) (b) \(c=\cfrac{b}{2a}\) (c) \(c= \cfrac{-b^2}{4a}\) (d) \(c = \cfrac{b^2}{4a}\)
26. For the equation \(5x^2+9x+3=0\) , if the roots are \(α\) and \(β\), then what is the value of \(\cfrac{1}{α}+\cfrac{1}{β}\) ?
(a) 3 (b) -3 (c) \(\cfrac{1}{3}\) (d) -\(\cfrac{1}{3}\)
27. For the equation \( 3x^2 + 8x + 2 = 0 \), if the roots are \( \alpha \) and \( \beta \), then what is the value of \( \frac{1}{\alpha} + \frac{1}{\beta} \)?"
(a) -\(\cfrac{3}{8}\) (b) \(\cfrac{2}{3}\) (c) -4 (d) 4
28. For the quadratic equation \(x^2 - bkx + 5 = 0\), if one of the roots is 5, then the value of \(k\) will be.
(a) \(-\cfrac{1}{2}\) (b) -1 (c) 1 (d) 0
29. If \(α\) and \(β\) are the roots of the equation \(3x^2 + 8x + 2 = 0\), find the value of \(\cfrac{1}{α} + \cfrac{1}{β}\).
(a) \(-\cfrac{3}{8}\) (b) \(\cfrac{2}{3}\) (c) -4 (d) 4
30. If the roots of the quadratic equation \(ax^2+bx+c=0\) are real and unequal, the value of \(b^2-4ac\) will be:
(a) >0 (b) <0 (c) 0 (d) None of these
