Question
A mother has decided to sum and product the ages of her children Ishan and Anushka. The sum and product of their ages are 18 and 56, respectively. The solution of which quadratic equation gives the possible ages of Ishan and Anushka?
The correct answer is
$x^2 - 18x + 56 = 0$
Finding Quadratic Equation for Children's Ages
Let the ages of Ishan and Anushka be the roots ($\alpha$ and $\beta$) of a quadratic equation. We are given:
- Sum of ages: $\alpha + \beta = 18$
- Product of ages: $\alpha \times \beta = 56$
A quadratic equation can be formed using its roots with the formula:
$ x^2 - (\text{sum of roots})x + (\text{product of roots}) = 0 $
Substituting the given sum and product into the formula:
$ x^2 - (18)x + (56) = 0 $
This simplifies to:
$ x^2 - 18x + 56 = 0 $
Comparing this equation with the given options, we find it matches option 4.
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