Theory question 112
Quadratic Equations(a) Derive an equation whose coefficients are integers and which has roots of 1/2 and −7. (b) Three years ago a father was four times as old as his daughter is now. The product of their present ages is 430. Calculate the present ages of the daughter and the father.
Show the model answer
Model answer
(a) (x − ½)(x + 7) = 0 ⇒ (2x − 1)(x + 7) = 0 ⇒ 2x2 + 13x − 7 = 0.
(b) Let the daughter be d and the father f years old now.
f − 3 = 4d and fd = 430.
(4d + 3)d = 430 ⇒ 4d2 + 3d − 430 = 0 ⇒ (d − 10)(4d + 43) = 0 ⇒ d = 10.
Daughter 10 years, father 43 years.
Explanation
Reject the negative root: an age can't be negative.