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प्रश्न
If x = −3 and x = `2/3` are solutions of quadratic equation mx2 + 7x + n = 0, find the values of m and n.
उत्तर
Step 1: Sum and product of roots
Sum of roots = `-b/a, "Product of roots" = c/a`
- Roots: x1 = −3, x2 = `2/3`
- Coefficients: a = m, b = 7, c = n
Step 2: Calculate sum and product of roots
`x_1 + x_2 = -3 + 2/3 = -9/3 + 2/3 = -7/3`
Using Sum of roots = `−b/a`
`-7/3 = -7/m`
Equating the numerators, m = 3
Product of roots: `x_1xxx_2 = (-3)xx 2/3 = -2`
Using Product of roots = `c/a`
`-2 = n/m`
Substitute m = 3
`-2 = n/3 => n=-6`
m = 3, n = −6
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