Question

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

Answer 1

Answer:

yeh kya faltu ke question aap puch rahe ho Anshu

Answer 2

Question:-

From the quadratic equations from the roots 3and -10

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,

• $Some\:of\:roots=\frac{-b}{a}$

• $Product\:of\:roots=\frac{c}{a}$

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.