Question

what is the degree polynomial of 4 x³+3x²-2x​

Answer 1

Substituting x = 2 in the given polynomial, we get,

(2)³ — 3(2)² — 4(2) + 12

= 8 — 12 — 8 + 12

= 0

So x = 2 is a zero of the given polynomial.

Substituting x = 3 in the given polynomial, we get,

(3)³ — 3(3)² — 4(3) + 12

= 27 — 27 — 12 + 12

= 0

So x = 3 is a zero of the given polynomial.

Since x = 2 and x = 3 are the zeros of the polynomial so (x—2) and (x—3) will be the factors of the polynomial.

Let third zero be a, so we can write

(x—2)(x—3)(x—a) = x³ — 3x² — 4x + 12

=> (x² — 5x + 6)(x—a) = x³ — 3x² — 4x + 12

=> x³ - 5x² + 6x - ax² + 5ax - 6a = x³ - 3x² - 4x + 12

Comparing the constant terms, we get

—6a = 12

=> a = —2

So the third zero is —2.