Question

find a quadratic polynomial the sum and product of whose zeros are 2 and -3/5 respectively ​

Answer 1

Answer:

x²-2x-3/5

Multiple the polynomial by 5

5x²-10x-3 is your answer

Hope this helps you please mark my answer as brainliest

Answer 2

Answer:

The required quadratic polynomial is

$\boxed{\red{\sf\:5x^{2}\:-\:10x\:-\:3}}$

Step-by-step-explanation:

We have given the sum and product of the zeroes of a quadratic polynomial.

$\sf\:Sum\:of\:zeroes\:=\:\alpha\:+\:\beta\:=\:2\\\\\sf\:Product\:of\:zeroes\:=\:\alpha\:.\:\beta\:=\:-\:\frac{3}{5}\\\\\sf\:Now,\:we\:know\:that\\\\\sf\:The\:required\:quadratic\:polynomial\:is\:in\:form\\\\\pink{\sf\:x^{2}\:-\:(\:\alpha\:+\:\beta\:)\:x\:+\:(\:\alpha\:.\:\beta\:)}\\\\\implies\sf\:x^{2}\:-\:(\:2\:)\:x\:+\:(\:-\:\frac{3}{5}\:)\\\\\implies\sf\:x^{2}\:-\:2x\:-\:\frac{3}{5}\\\\\implies\boxed{\red{\sf\:5x^{2}\:-\:10x\:-\:3}}\sf\:\:\:[\:Multiplying\:both\:sides\:by\:5\:]$

Additional Information:

1. Quadratic Equation :

An equation having a degree '2' is called quadratic equation.

The general form of quadratic equation is

ax² + bx + c = 0

Where, a, b, c are real numbers and a ≠ 0.

2. Roots of Quadratic Equation:

The roots means nothing but the value of the variable given in the equation.

3. Methods of solving quadratic equation:

There are mainly three methods to solve or find the roots of the quadratic equation.

A) Factorization method

B) Completing square method

C) Formula method

4. Formula to solve quadratic equation:

$\boxed{\red{\sf\:x\:=\:\dfrac{-\:b\:\pm\:\sqrt{b^{2}\:-\:4ac}}{2a}}}$