Question

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

Answer 1

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.

$\tt \star \: \: \: \: \: a {x}^{2} + bx + c = 0.$

Where as,

a = 1.

b = 7.

c = - 30.

So,

$\tt \bullet \: \: \: \: \: Sum \: of \: roots= \dfrac{ - b}{a}$

$\tt \bullet \: \: \: \: \: Product \: of \: roots = \dfrac{c}{a}$

Also,

α = 3. ( given )

β = - 10. ( given )

Putting given value.

> Sum Of roots.

$\tt \mapsto \alpha + \beta = \dfrac{ - b}{a}$

$\tt \mapsto 3 + ( - 10) = \dfrac{ - 7}{1}$

$\tt \mapsto - 7= - 7$

LHS = RHS.

____________________________

> Product Of roots.

$\tt \mapsto \alpha \beta = \dfrac{ c}{a}$

$\tt \mapsto 3 \times ( - 10) = \dfrac{ - 30}{1}$

$\tt \mapsto - 30 = - 30.$

LHS = RHS.

Answer 2

Answer:

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.

$\tt \star \: \: \: \: \: a {x}^{2} + bx + c = 0.⋆ax </p><p>2</p><p> +bx+c=0.$

Where as,

a = 1.

b = 7.

c = - 30.

So,

$\tt \bullet \: \: \: \: \: Sum \: of \: roots= \dfrac{ - b}{a}∙Sumofroots= </p><p>a</p><p>−b$

$\tt \bullet \: \: \: \: \: Product \: of \: roots = \dfrac{c}{a}∙Productofroots= </p><p>a</p><p>c$

Also,

α = 3. ( given )

β = - 10. ( given )

Putting given value.

> Sum Of roots.

$\tt \mapsto \alpha + \beta = \dfrac{ - b}{a}↦α+β= </p><p>a</p><p>−b$

$\tt \mapsto 3 + ( - 10) = \dfrac{ - 7}{1}↦3+(−10)= </p><p>1</p><p>−7</p><p>$

$tt \mapsto - 7= - 7↦−7=−7$

LHS = RHS.

____________________________

> Product Of roots.

$\tt \mapsto \alpha \beta = \dfrac{ c}{a}↦αβ= </p><p>a</p><p>c$

$\tt \mapsto 3 \times ( - 10) = \dfrac{ - 30}{1}↦3×(−10)= </p><p>1</p><p>−30</p><p>$

$\tt \mapsto - 30 = - 30.↦−30=−30.$

LHS = RHS.