Question

sum and product of the zeros of a quadratic polynomial p(x) =ax2+bx-4 are 1/4 and -1 respectively.then find the values of a and b​

Answer 1

Answer:

sum =1/4

so -b/a =1/4

product =-4/a=-1

so a=4

and

-b =1

b =-1

4,-1 is a,b .plS mark as BRAINLIEST IF LIKED BY YOU

Answer 2

Values are $a = 4 \: and \: b = - 1$

Given:

• A quadratic polynomial $a {x}^{2} + bx - 4$.
• Sum and product of the zeros of a quadratic polynomial are 1/4 and -1 respectively.

To find:

• Find the values of a and b.

Solution:

Concept to be used:

• A quadratic polynomial can be expressed as it's sum of zeros and product of zeros, as follows:$\bf {x}^{2} - ( \text{\bf sum of zeros})x + ( \text{\bf product of zeros})$
• The standard quadratic polynomial is $\bf a {x}^{2} + bx + c ,a\neq0$

Step 1:

It is given that

Sum of zeros: 1/4

Product of zeros: -1

Put the values,

${x}^{2} - ( \text{\bf sum of zeros})x + ( \text{\bf product of zeros})$

The polynomial is $\bf {x}^{2} - \frac{1}{4} x - 1$

Step 2:

Simplify the polynomial.

Simplify the quadratic polynomial and compare with the given polynomial.

Multiply the polynomial by 4.

$\bf 4 {x}^{2} - x - 4$

Compare the above polynomial with the given polynomial.

It is clear that,

$a = 4 \\ b = - 1$

Thus,

Values are $\bf a = 4 \: and \: b = - 1$

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