Question

Find the value of polynomial p(x)=2x^4-3x^3-4x+5 when x=2,-1/2,1/4 and -3

Answer 1

Solution :-

given,

→ p(x) = 2x^4 - 3x^3 - 4x + 5

so, at x = 2,

→ p(2) = 2(2)⁴ - 3(2)³ - 4(2) + 5

→ p(2) = 2*16 - 3*8 - 8 + 5

→ p(2) = 32 - 24 - 8 + 5

→ p(2) = 32 - 32 + 5

→ p(2) = 5

at x = (-1/2)

→ p(-1/2) = 2(-1/2)⁴ - 3(-1/2)³ - 4(-1/2) + 5

→ p(-1/2) = 2*(1/16) - 3*(-1/8) - (-2) + 5

→ p(-1/2) = (1/8) + (3/8) + 2 + 5

→ p(-1/2) = (4/8) + 7

→ p(-1/2) = (1/2) + 7 = 7(1/2)

at x = 1/4,

→ p(1/4) = 2(1/4)⁴ - 3(1/4)³ - 4(1/4) + 5

→ p(1/4) = 2*(1/256) - 3*(1/64) - 1 + 5

→ p(1/4) = (1/128) - (3/64) + 4

→ p(1/4) = (1 - 6 + 4)/128

→ p(1/4) = (-1/128)

at x = (-3),

→ p(-3) = 2(-3)⁴ - 3(-3)³ - 4(-3) + 5

→ p(-3) = 2*81 - 3*(-27) + 12 + 5

→ p(-3) = 162 + 81 + 17

→ p(-3) = 260

Learn more :-

JEE mains Question :-

https://brainly.in/question/22246812

. Find all the zeroes of the polynomial x4

– 5x3 + 2x2+10x-8, if two of its zeroes are 4 and 1.

https://brainly.in/question/39026698

Answer 2

Given:

p(x) = 2x⁴ - 3x³ - 4x + 5

x = 2, -1/2, 1/4 and -3

To find:

Find the value of polynomial p(x) = 2x⁴ - 3x³ - 4x + 5 when x = 2, -1/2, 1/4 and -3

Solution:

When x = 2

p(x) = 2x⁴ - 3x³ - 4x + 5

p(2) = 2×2⁴ - 3×2³ - 4×2 + 5

p(2) = 32 - 24 - 8 + 5

p(2) = 5

When x = -1/2

p(x) = 2x⁴ - 3x³ - 4x + 5

p(-1/2) = 2(-1/2)⁴ - 3(-1/2)³ - 4(-1/2) + 5

p(-1/2) = 1/8 + 3/8 + 2 + 5

p(-1/2) = (1 + 3 + 16 + 40) / 8

p(-1/2) = 60/8

p(-1/2) = 15/2

p(-1/2) = 7.5

When x = 1/4

p(x) = 2x⁴ - 3x³ - 4x + 5

p(1/4) = 2(1/4)⁴ - 3(1/4)³ - 4(1/4) + 5

p(1/4) = 1/128 - 3/64 - 1 + 5

p(1/4) = (1 - 6 - 128 + 640) / 128

p(1/4) = 507/128

When x = -3

p(x) = 2x⁴ - 3x³ - 4x + 5

p(-3) = 2(-3)⁴ - 3(-3)³ - 4(-3) + 5

p(-3) = 2×81 + 81 + 12 + 5

p(-3) = 162 + 81 + 12 + 5

p(-3) = 260