Question

Find the value of a and b, if 1 and -1 are zeroes of polynomial x4^+ax^3+2x^2- 3x+b​

Answer 1

ANSWER :–

GIVEN :–

A POLYNOMIAL x⁴ + ax³ + 2x² - 3x + b = 0 have to two roots which are 1 and -1 .

TO FIND :–

VALUES OF a and b .

SOLUTION :–

● IF 1 AND -1 ROOTS OF POLYNOMIAL THEN IT WILL SATISFY THE POLYNOMIAL .

● LET'S –

• PUT X = 1 =>

✍.... 1 + a + 2 - 3 + b = 0

✍ .... a + b = 0 .........(1)

• NOW PUT X = - 1 =>

✍.... 1 - a + 2 + 3 + b = 0

✍.... -a + b = -6 ..........(2)

● NOW ADD EQUATION (1) AND (2) —

➪ ( a + b ) + ( -a + b ) = -6

➪ 2 b = - 6

➪ b = - 3

● NOW FROM EQUATION (1) —

➪ a + ( - 3 ) = 0

➪ a = 3

✪✪✪ HENCE , a = 3 and b = - 3 ✪✪✪