Question

this question is Marathi but you can write your answer in English ​

Answer 1

The given roots are -3 and -7.

$\sf \: {x}^{2} - ( \alpha + \beta )x + ( \alpha \beta ) = 0$

Let α = -3 and β = -7,

${x}^{2} - \lgroup( - 3 ) + ( - 7) \rgroup x + ( - 3 \times - 7) = 0$

${x}^{2} - ( - 10)x + 21 = 0$

$\green{{x}^{2} + 10x + 21 = 0}$

Additional Information:

1) If roots of quadratic equation are given:

x²-(α+β)x + (αβ) = 0

2) α+β = - b/a

3) αβ = c/a

Quadratic equation can be solved by quadratic formula, complete square method, factorisation method.

Answer 2

★ प्रश्न :

ज्या वर्गसमीकरणाची मुळे -3, -7 आहेत असे वर्ग समीकरण तयार करा.

Step-by-step explanation:

★ सूत्र :

x² - (मुळांची बेरीज) x + मुळांचा गुणाकार = 0

समजा,

α = -3 आणि β = -7

• α = -3
• β = -7

α + β = (-3) + (-7) = -10

आणि

α × β = (-3) × (-7) = 21

• मिळणारे समीकरण,

x² - (मुळांची बेरीज) x + मुळांचा गुणाकार = 0

⇒ x² - (α + β) x + α × β = 0

⇒ x² - (-10) x + 21 = 0

⇒ x² + 10x + 21 = 0

∴ वर्ग समीकरण = x² + 10x + 21 = 0