Question

Line AB contains points A(4, 5) and B(9, 7). What is the slope of Aß?

Answer 1

Let the common root is ‘x’

Let the common root is ‘x’x2 + ax + b = 0 ……(1)

Let the common root is ‘x’x2 + ax + b = 0 ……(1)x2 + bx + a = 0 ……(2)

Let the common root is ‘x’x2 + ax + b = 0 ……(1)x2 + bx + a = 0 ……(2)Subtract equation (2) from (1), we get

Let the common root is ‘x’x2 + ax + b = 0 ……(1)x2 + bx + a = 0 ……(2)Subtract equation (2) from (1), we get(a – b)x + (b –a) = 0

Let the common root is ‘x’x2 + ax + b = 0 ……(1)x2 + bx + a = 0 ……(2)Subtract equation (2) from (1), we get(a – b)x + (b –a) = 0⇒ x = (a-b)/(a-b) = 1

Let the common root is ‘x’x2 + ax + b = 0 ……(1)x2 + bx + a = 0 ……(2)Subtract equation (2) from (1), we get(a – b)x + (b –a) = 0⇒ x = (a-b)/(a-b) = 1⇒ x = 1

Let the common root is ‘x’x2 + ax + b = 0 ……(1)x2 + bx + a = 0 ……(2)Subtract equation (2) from (1), we get(a – b)x + (b –a) = 0⇒ x = (a-b)/(a-b) = 1⇒ x = 1⇒ {1 + a + b = 0} (From equation (1))

Let the common root is ‘x’x2 + ax + b = 0 ……(1)x2 + bx + a = 0 ……(2)Subtract equation (2) from (1), we get(a – b)x + (b –a) = 0⇒ x = (a-b)/(a-b) = 1⇒ x = 1⇒ {1 + a + b = 0} (From equation (1))⇒ a + b = –1