1. Show that X+1 and 2x-3 are factor of 2x³-9x²+X+12
2. for what values of a is 2x³ +ax²+11x+a+3 exactly divisible by (2x-1)
3. If x²-1 is a factor of ax⁴+bx³+cx²+dx+e, show that a+c+e=b+d=0
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Answers
1.
We need to check if (2x-3) is a factor of the polynomial 2x³-9x²+x+12
Fir.st equate 2x-3 to 0 and find value of x.
2x - 3 = 0
⇒ 2x = 3
⇒ x = 3/2
If x=3/2 is a root of the polynomial, then (2x-3) is a factor.
at x=3/2, value of polynomial is
2(3/2)³ - 9(3/2)² + 3/2 + 12
= 2×(27/8) - 9×(9/4) + 3/2 + 12
= 27/4 - 81/4 + 3/2 + 12
= (27 - 81 + 6 + 48)/4
= (81-81)/4
= 0
So 3/2 is a root of the polynomial. Hence (2x-3) is a factor of the polynomial.
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Step-by-step explanation:
Strong acid is an acid that ionizes completely in aqueous solution. It always loses a proton (H+) when dissolved in water. Weak acid is an acid that ionizes partially in a solution. It gives off only a few of its (H+) atoms when dissolved in water.
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