Question

find a .... m and n are the zeroes of the polynomial p(x)=ax2-35x=12 / m2+n2=1

Answer 1

m and n are zeroes of the given polynomial, P(x) : ax² - 35x = 12, it is also given that m² + n² = 1

resolve the given polynomial in standard from, i.e., ax² - 35x - 12

here coefficient of x² = a

coefficient of x = -35

constant = -12

now sum of zeroes = - coefficient of x/coefficient of x²

or, m + n = -(-35)/a

or, m + n = 35/a .......(1)

product of zeros = constant/coefficient of x²

or, mn = -12/a .......(2)

now, m² + n² = 1

or, (m + n)² - 2mn = 1

from equations (1) and (2),

or, (35/a)² - 2 × (-12/a) = 1

or, 1225/a² + 24/a = 1

or, 1225 + 24a = a²

or, a² - 24a - 1225 = 0

or, a² - 49a + 25a - 1225 = 0

or, a(a - 49) + 25(a - 49) = 0

or, (a + 25)(a - 49) = 0

or, a = 49, -25

hence, value of a = 49, -25