Question

If x = -2 is a root of the polynomial P(x) = -2x
4
- 7x
3
- 3x
2
- tx - 10, then find the

value of t.

Answer 1

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Answer 2

Answer:

t = -1

Step-by-step explanation:

p(x)= -2x⁴ -7x³ -3x² -t(-2) -10

g(x)= -2

p(-2)= -2(-2)⁴ -7(-2)³ -3(-2)² -t(-2) -10 =0

= -2(16) -7(-8) -3(4) -t(-2) -10 =0

= 32 +56 -12 -2t -10 =0

= 56 -54 -2t =0

= 2 -2t =0

= -2t =-2

= t = -2/+2 = -1

Verification:  

p(-2)=  -2(-2)⁴ -7(-2)³ -3(-2)² -(-1)(-2) -10 =0

      = -2(16) -7(-8) -3(4) -2 -10 =0

= -32 +56 -12 -2 -10 =0

= 24 -24 =0