Question

Solve quadratic equations m2-14m+13=0 by factorisation

Answer 1

Answer :

$\text{The zeroes of the polynomial are 1 and 13}$

Step-by-step explanation :

Given quadratic equation,

  m² - 14m + 13 = 0

=> It is of the form ax² + bx + c

    a = 1, b = -14, c = 13

a - coefficient of x²

b - coefficient of x

c - constant term

By sum-product pattern,

>> Find the product of quadratic term [ax²] and constant term [c]

 = m² × 13

 = 13m²

>> find the factors of "13m²" in pairs

    => (m) (13m)

    => (-m) (-13m)

>> From the above, find the pair that adds to get linear term [bx]

   - m - 13m = -14m

>> So, split -14m as -m and -13m

     m² - 14m + 13 = 0

     m² - m - 13m + 13 = 0

>> Find the common factor

      m(m - 1) - 13(m - 1) = 0

         (m - 1) (m - 13) = 0

=> (m - 1) = 0 ; m = +1

=> (m - 13) = 0 ; m = +13

The zeroes of the polynomial are 1 and 13.