Page 15 - 10-Math-2 THEORY OF QUADRATIC EQUATIONS

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Example 3: Find h, if the roots of the equation x2 - hx + 10 = 0 differ
by 3.
Solution: Let a and a - 3 be the roots of x2 - hx + 10 = 0.

Putting value of a from equation (i) in equation (ii), we get

(d) Roots satisfy a given relation
(e.g. 2a + 5b = 7, where a, b are the roots of a given equation).

Example 4: Find p, if the roots a, b of the equation x2 - 5x + p = 0,
satisfy the relation
2a + 5b = 7.

Solution: If a, b are the roots of the equation x2 - 5x + p = 0.

Put the value of b from equation (i) in equation (iii) Version 1.1
2a + 5(5 - a) = 7
2a + 25 - 5a = 7 or -3a = 7 - 25, that is
-3a = -18 ⇒ a = 6 (iv)
b = 5 - 6 = -1 Use (i) and (iv)
Put the values of a and b in eq. (ii)

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