Question

if (x-1)is a factor of p(x)=kx2+x-3 what is the value of k?find the other factor of p(x).




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Answer 1

EXPLANATION.

(x - 1) is the factor of the equation,

⇒ p(x) = kx² + x - 3.

As we know that,

x - 1 is the zeroes of the polynomial.

⇒ x - 1 = 0.

⇒ x = 1.

Put the value of x = 1 in equation, we get.

⇒ k(1)² + (1) - 3 = 0.

⇒ k + 1 - 3 = 0.

⇒ k - 2 = 0.

⇒ k = 2.

                                                                                     

MORE INFORMATION.

Quadratic expression.

A polynomial of degree two of the form ax² + bx + c (a ≠ 0) is called a quadratic expression in x.

The quadratic equation.

ax² + bx + c = 0 (a ≠ 0) has two roots, given by.

α = -b +√D/2a.

β = -b - √D/2a.

D = discriminant of the equation.

D = b² - 4ac.

Answer 2

${\large{\bold{\rm{\underline{Question}}}}}$

★ If (x-1) is a factor of p(x) = kx²+x-3. What is the value of k?

${\large{\bold{\rm{\underline{Given \; that}}}}}$

${\sf{:\implies (x-1) \: is \: a \: factor \: of \: p(x) = kx^{2} +x -3}}$

${\large{\bold{\rm{\underline{To \; find}}}}}$

${\sf{:\implies Value \: of \: k}}$

${\large{\bold{\rm{\underline{Solution}}}}}$

${\sf{:\implies Value \: of \: k \: = 2}}$

${\large{\bold{\rm{\underline{Full \; Solution}}}}}$

~ As it's already given that,

${\sf{:\implies (x-1) \: is \: a \: factor}}$

${\sf{:\implies p(x) \: = kx^{2}+x-3}}$

~ We already know that ${\tt{x-1}}$ is the zero of the polynomial equation. Henceforth,

${\sf{:\implies x-1 \: = 0}}$

${\sf{:\implies x \: = 0+1}}$

${\sf{:\implies x \: = 1}}$

~ Now let's imply value of x in our equation..!

${\sf{:\implies k(1)^{2}+(1)-3 = 0}}$

${\sf{:\implies k(1)-3 = 0}}$

${\sf{:\implies k + 1 - 3 = 0}}$

${\sf{:\implies k - 2 = 0}}$

${\sf{:\implies k = 0 +2}}$

${\sf{:\implies k = +2}}$

${\large{\bold{\rm{\underline{Additional \; knowledge}}}}}$

Knowledge about Quadratic equations -

★ Sum of zeros of any quadratic equation is given by ➝ α+β = -b/a

★ Product of zeros of any quadratic equation is given by ➝ αβ = c/a

★ A quadratic equation have 2 roots

★ ax² + bx + c = 0 is the general form of quadratic equation