Question

polynomial very hard question...........if the product of the zeros of a quadratic polynomial f(x)=x²-4x+K is 3 .find the value of K ..... brainliest yr ans.awarded don't make spams otherwise reported​

Answer 1

→ Given ←

The product of the zeros of a quadratic polynomial f(x) = x²- 4x + K is 3.

◙ If α and β are the zeros of f(x) = x²- 4x + K, then αβ = 3.

$\rule{180}2$

→ To Find ←

The value of K.

$\rule{180}2$

→ Solution ←

As we know that,

Product of zeros = c/a.

In the given polynomial f(x),

a = 1, b = -4 & c = K.

Putting the values :-

αβ = c/a

⇒3 = K/1

⇒K = 3

◘ Hence, the value of K is 3.

$\rule{180}2$

Additional information :-

• For the sum of zeros given, the relationship with the coefficient can be defined as :-

α + β = -b/a

• "a" is the coefficient of x².

• "b" is the coefficient of x.

• "c" is the constant term.

Note that, these are applicable for only quadratic equations. For other type of equations, the relationship varies.

Answer 2

Given that :-

• Quadratic equation - x² -4x +k = 0

• Product of its zeros - 3 .

To Find :-

• Value of k

Solution :-

General form of Equation - ax² + bx + c = 0

Product of Zeros is equivalent to -

$\boxed{\sf{\red{\implies \: Product \: = \dfrac{C}{a} }}}$

Here a = 1 , b = -4 and C = k

Using the formula mentioned above :-

$\sf{\implies \: Product \: = \dfrac{C}{a} }$

$\sf{\implies \: 3 \: = \dfrac{k}{1} }$

$\sf{\implies \: 3 \times 1 \: = k}$

Value of K = 3 .