Question

find the sum and product of the roots of 3x-^5x+2=0​

Answer 1

EXPLANATION.

Quadratic equation.

⇒ 3x² - 5x + 2 = 0.

As we know that,

Sum of the zeroes of quadratic equation.

⇒ α + β = -b/a.

⇒ α + β = -(-5)/3 = 5/3.

Products of the zeroes of the quadratic equation.

⇒ αβ = c/a.

⇒ αβ = 2/3.

As we know that,

Formula of quadratic polynomial.

⇒ x² - (α + β)x + αβ.

⇒ x² - (5/3)x + 2/3 = 0.

⇒ 3x² - 5x + 2 = 0.

                                                                                                                 

MORE INFORMATION.

Quadratic expression.

A polynomial of degree two of the form ax² + bx + c (a ≠ 0) is called a quadratic expression in x.

The quadratic equation.

⇒ α = -b + √D/2a.

⇒ β = -b - √D/2a.

⇒ D = Discriminant.

⇒ D = b² - 4ac.

Answer 2

${\boxed{\underline{\tt{ \orange{Required \: \: answer:-}}}}}$

★GIVEN:-

• $\sf{Equation = 3x^2 -5x +2 =0}$

★TO FIND:-

• Sum of roots

• product of roots

★SOLUTION:-

Our Standard Quadratic equation is-

$\: \: \: \: \: \: \: \: \: \: \: : \implies \: { \boxed{ \underline{ \sf{ax^2 + bx + c}}}}$

$: \longrightarrow \: \sf{Sum \: \: of \: \: Roots \: = \: \frac{ - b}{a} }$

$: \longrightarrow \sf{Product \: \: of \: \: Roots \: = \: \frac{c}{a} }$

So on Comparing,

$: \longrightarrow \sf{3x^2 -5x + 2=0}$

$: \longrightarrow \sf{sum \: \: of \: \: roots \: = \: \frac{ - ( - 5)}{3} }$

$: \longrightarrow \sf{sum \: \: of \: \: roots \: = \: \frac{ 5}{3} }$

$:\longrightarrow\sf{Product \: \: of \: \: Roots \: = \: \frac{c}{a} }$

$:\longrightarrow\sf{Product \: \: of \: \: Roots \: = \: \frac{2}{3} }$

so, sum is 5/4

and product is 2/3

★MORE TO KNOW:-

• $D = b^2 - 4ac$

• $x = \frac{-b ± \sqrt{D} }{2a}$

• Standard form of equation:- ax^2 + bx + c= 0

FACTORING FORMULA'S

• ${a}^{2} - {b}^{2} = (a - b)(a + b)$

• ${a}^{3} -{b}^{3} = (a - b)( {a}^{2} + ab + {b}^{2} </strong><strong>$

• ${a}^{3} + {b}^{3} = (a + b)( {a}^{2} - ab + {b}^{2}</strong><strong>$

• ${a}^{4} - {b}^{4} = (a - b)(a + b)( {a}^{2} + {b}^{2})$