Question

Find the quadratic polynomial for the zeroes Alfa, beta given in each case is 1/4,-1​

Answer 1

Answer:

The formula u will be using will be,

x² - (sum of products) x + (product of roots).

Step-by-step explanation:

Sum of roots will be (1/4)+(-1).

→(-3/4)

Product of roots will be (1/4)(-1)

→(-1/4)

Putting in the formula,

→ x² - (-3/4) x + (-1/4)

→ x² + (3x/4) -1/4

Now, multiplying the whole polynomial by4 we get,

→ 4x² + 3x -1

So, the required quadratic polynomial with given zeroes will be 4x² + 3x - 1

Answer 2

$\Large \rm \orange {✧Given✧}$

A quadratic polynomial whose zeroes $\sf \alpha , \beta$ are $\sf \cfrac{1}{4} , -1$.

$\Large \rm \orange {✧To~find✧}$

We have to find the quadratic equation which has the above mentioned zeroes.

$\Large \rm \orange {✧Solution✧}$

A quadratic equation can be given by :-

$\sf \red {✧~~x^2-(\alpha + \beta)x+(\alpha \beta)~~✧ }$

$\bullet ~~\sf Sum ~of~zeroes: \\ \sf = \alpha + \beta \\ \sf \: \: \: \: \: \: = \frac{1}{4 } + ( - 1) \\ \sf = \frac{ - 3}{4}$

$\bullet ~~\sf Product~of~zeroes : \\ \sf= \alpha \beta \\ \sf \: \: \: \: \: \: \: = \frac{1}{4} ( - 1) \\ \sf = \frac{ - 1}{4}$

Substituting in the formula :-

$\red \leadsto \sf x^2-( \cfrac{-3}{4} )x+( \cfrac{-1}{4} )$

$\red \leadsto \sf 4x^2 + 3x - 1$

$\sf \green {\therefore~The~quadratic~polynomial~is~4x^2+3x-1.}$

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