Question

If the sum and product of roots of a quadratic equation are - 7/2 and 5/2
respectively, then

the equation is __________.​

Answer 1

SOLUTION:-

Given

⠀⠀ • Sum of zeros = -7/2

⠀⠀ • Product of zeros = 5/2

To Calculate

⠀⠀ • Equation?

Explanation

⠀⠀ • Sum of zeros = -7/2

⠀⠀ • Product of zeros = 5/2

⠀⠀ For Quadratic polynomial ⤵️

$= \: x {}^{2} - ( \alpha + \beta )x + \alpha \beta$

Putting values,

=>> x²- (-7/2)x + 5/2=0

=>> x²+7/2x+5/2=0

Take LCM

=>> 2x²+7x+5 /2 =0

=>> 2x²+7x+5=0

Hence,

⠀⠀ • Equation is 2x²+7x+5

______________________________

Answer 2

Given,

Sum of roots $\[ = - \frac{7}{2}\]$

Product of roots $\[ = \frac{5}{2}\]$

Solution,

Consider the roots of quadratic equations are $\[\alpha ,\beta \]$

The quadratic polynomial is $\[{x^2} + \left( {\alpha + \beta } \right)x + \alpha \beta = 0\]$

$\[{x^2} + \left( {\frac{{ - 7}}{2}} \right)x + \frac{5}{2} = 0\]$

$\[ \Rightarrow 2{x^2} - 7x + 5 = 0\]$

Hence the equation is $\[2{x^2} - 7x + 5 = 0\]$