Question

Find a quadratic polynomial whose zeroes are -3 and 2.​

Answer 1

Answer:

x²+x-6=0

Step-by-step explanation:

hope it help u out please mark it brainliest and follow me

Answer 2

Given :-

• Zeroes of quadratic polynomial are -3 and 2

To Find :-

• Required quadratic polynomial

Solution :-

We are given, Zeros of quadratic polynomial are -3 and 2.

$\boxed{\pink{\sf Sum\ of\ the\ zeroes=\frac{-coefficient\ of\ x}{coefficient\ of\ x^{2}}}}$

$\qquad\leadsto\quad \sf -3 +2$

$\qquad\leadsto\quad \sf -1$

$\boxed{\pink{\sf Product\ of\ the\ zeroes=\frac{Constant}{coefficient\ of\ x^{2}}}}$

$\qquad\leadsto\quad \sf -3 \times 2$

$\qquad\leadsto\quad \sf -6$

Quadratic polynomial :-

$\qquad$ ☀️ x²-(sum of zeros)x+product of zeros 

$\qquad\leadsto\quad \sf x²- (-1) x+ (-6)$

$\pink{\qquad\leadsto\quad \sf x²+x -6}$

⠀⠀⠀⠀¯‎¯‎‎‎¯‎¯¯‎¯‎‎‎¯‎‎‎¯‎¯‎¯‎‎¯‎‎‎¯‎¯‎‎‎¯‎‎‎¯‎¯‎¯‎‎‎¯‎‎¯‎‎‎¯‎‎¯‎¯‎‎‎¯‎‎‎¯‎¯‎¯‎‎¯‎¯‎‎¯‎¯¯‎¯‎¯‎‎‎¯‎¯‎‎‎¯‎‎‎¯‎‎‎¯‎‎‎¯‎

$\qquad \qquad \:\bigstar \:\:\underline {\pmb{ \: Know \: More \:\::-}}\:$

The quadratic formula is _

$\boxed{\pmb {\mathfrak { x = \dfrac{ - b \pm \sqrt{ b^2 - 4ac }}{ 2a} }}}$

It can be written as :-

$\qquad$ $\pmb {\mathfrak{ \alpha = \dfrac{-b + \sqrt{b^2 - 4ac }}{ 2a }} }$

$\qquad$ $\pmb {\mathfrak{\beta = \dfrac{ - b - \sqrt{ b^2 - 4ac }}{ 2a } }}$

Where:-

• α , β are the roots of the quadratic equation . b² - 4ac is a discriminate .

The conditions are as follows :-

$\qquad$ ☀️If D = 0

• The roots are equal and real .

$\qquad$ ☀️If D > 0

• The roots are unequal and rational ( if it is a perfect square )

$\qquad$ ☀️If D > 0

• The roots are distinct and irrational ( if it is not a perfect square )

$\qquad$ ☀️If D < 0

• The roots are unequal and imaginary .

⠀⠀⠀⠀¯‎¯‎‎‎¯‎¯¯‎¯‎‎‎¯‎‎‎¯‎¯‎¯‎‎¯‎‎‎¯‎¯‎‎‎¯‎‎‎¯‎¯‎¯‎‎‎¯‎‎¯‎‎‎¯‎‎¯‎¯‎‎‎¯‎‎‎¯‎¯‎¯‎‎¯‎¯‎‎¯‎¯¯‎¯‎¯‎‎‎¯‎¯‎‎‎¯‎‎‎¯‎‎‎¯‎‎‎¯‎