Question

find the equation whoose roots are 3/7 and -4/5​

Answer 1

Answer:

Obtain a quadratic equation whose roots are –3 and –7.

SOLUTION

α = -3 , β =-7

α + β = -3-7 =-10

αβ = (-3)(-7)= 21

x2 - (α+β)x + αβ =0

x2 - (-10x) +21 = 0

x2 + 10x +21 = 0

Concept: Quadratic Equations Examples and Solutions

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2018-2

here is an example for you...

hopes it helps you...

Answer 2

Answer:

$\boxed{\bf {35x}^{2} + 13x - 12 = 0}$

Step-by-step explanation:

$\bf \: Let \: \alpha = \frac{3}{7} \: or \: \: \: \beta = \frac{ - 4}{5} \\ \\ \bf \implies: \alpha + \beta = \frac{3}{7} + ( \frac{ -4 }{5} ) \\ \\ \bf \implies: \alpha + \beta = \frac{15 - 28}{35} \\ \\ \bf \implies: \alpha + \beta = \frac{ - 13}{35} \\ \\ \alpha \times \beta = \frac{3}{7} \times \frac{ - 4}{5} \\ \\ \bf \implies: \alpha \times \beta = \frac{ - 12}{35} \\ \\ \boxed{\tt\red{now \: quadratic \: equtation}} \\ \sf {x}^{2} - ( \alpha + \beta )x + \alpha \times \beta = 0 \\ \\ \bf \implies: {x}^{2} - ( - \frac{13}{35} ) + ( - \frac{12}{35} ) = 0 \\ \\ \bf \implies: {x}^{2} + \frac{13}{35}x - \frac{12}{35} = 0 \\ \\ \bf \implies: {35x}^{2} + 13x - 12 = 0$