Question

From the quadratic equations from the roots 3and -10
explanation​






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Answer 1

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Step-by-step explanation: paagal sallay

Answer 2

Answer:

x² + 7x - 30 = 0.

SolutioN :

Let,

• Sum Of Zeros ( α + β )
• Product Of Zeros ( α × β )

For Sum of roots.

→ a + b

→ 3 - 10

→ - 7

For Product of roots.

→ ab

→ 3 × - 10

→ - 30.

_____________________

We have, Formula.

→ K [ x² - Sx + P ]

Where as,

• K Content terms.
• P Product of roots.
• S Sum of roots.

→ K[ x² - ( - 7 )x + ( - 30 ) ]

→ K[ x² + 7x - 30 ]

Therefore, the required quadratic equation is x² + 7x - 30.

_______________________________

More InformatioN :

We have, Quadratic Equation.

★ x² + 7x - 30 = 0.

Compare With General Equation.

★$ax^{2} +bx+c=0$

Where as,

• a = 1.
• b = 7.
• c = - 30.

So,

        Sums of roots$=\frac{-b}{a}$

        Product of roots$=\frac{c}{a}$

Also,

• α = 3. ( given )
• β = - 10. ( given )

Putting given value.

> Sum Of roots.

$\alpha +\beta =\frac{-b}{a} \\\\3+(-10)=\frac{-7}{1} \\\\-7=-7$

LHS = RHS.

____________________________

> Product Of roots.

$\alpha \beta =\frac{c}{a} \\\\3*(-10) =\frac{-30}{1} \\\\-30=-30$

LHS = RHS.