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