Question

guys please help me with this question and whoever will give me the answer I will mark them as brainliest but I want step by step explanation and I don't want and useless answers ​

Answer 1

$\bf\underline{\underline{\green{SOLUTION:-}}}$

Given

• p(x) = 2x³+px²-x+q
• g(x) = (x-2),(x+1)

To Calculate

• Value of p and q

Step by step explanation

• p(x) = 2x³+px²-x+q ( Given)
• g(x) = x-2

⠀⠀⠀⠀⟹ x-2=0

⠀⠀⠀⠀⟹ x=2

Putting x= 2 in p(x)

• p(x) = 2x³+px²-x+q=0

⟹ 2×(2)³+p×(2)²-2+q =0

⟹ 2×8+p×4-2+q=0

⟹ 16+4p-2+q=0

⟹ 4p+q+14=0

⟹ 4p+q= -14 _____________(1)

• p(x) = 2x³+px²-x+q
• g(x) = x+1

⠀⠀⠀⟹ x+1=0

⠀⠀⠀⟹ x=-1

Putting x=-1 in p(x)

• p(x) = 2x³+px²-x+q=0

⟹ 2×(-1)³+p×(-1)²-(-1)+q=0

⟹ 2×(-1)+p×1+1+q=0

⟹ -2+p+1+q=0

⟹ p+q-1=0

⟹ p+q=1_________(2)

On Subtracting eq 2 from 1

4p+q=-14

p+q= 1

________

3p= -15

p= -15/3

${\boxed{\red{\tt{P= -5}}}}$

Putting value of p in eq 2

• p+q=1

⟹ -5+q=1

⟹ q= 1+5

${\boxed{\red{\tt{q= 6 }}}}$

$\bf\underline{\underline{\green{HENCE:-}}}$

• p= -5
• q= 6