Question

5.25 Submit SINGLE SELECT Last Sync: 05:06 PM Q6 of 60 Mark for review If a,ß are roots of 3x2 – 5x + 7 = 0, then a? +B2 + = Clear Responseइफ अल्फा एंड बीटा और रूट्स ऑफ थ्री एक्स स्क्वायर माइनस फाइव 1 प्लस 7 इक्वल टू जीरो वन एस अल्फा स्क्वायर प्लस बी स्क्वायर इक्वल टू ​

Answer 1

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It has given that, α and β are roots of the equation 3x² + 5x - 7 = 0

We have to find the value of αβ

Solution :

1st method : product of roots = constant/coefficient of x² = c/a

= (-7)/3

2nd method :

let's solve equation 3x² + 5x - 7 = 0

x = {-b ± √(b² - 4ac)}/2a

here, b = 5, a = 3 and c = -7

so, x = {-5 ± √(5² + 4 × 3 × 7)}/2(3)

= {-5 ± √(25 + 84)}/6

= {-5 ± √109}/6

so, (-5 + √109)/6 and (-5 - √109)/6 are roots of equation.

so we assume α = (-5 + √109)/6 and β = (-5 - √109)/6

now, αβ = (-5 + √109)/6 × (-5 - √109)/6

= {(-5)² - (√109)²}/36

= {25 - 109}/36

= -84/36

= -7/3