Question

the sum of two roots of quadratic equation is 5 and sum of their cude is 35 find the equation ​

Answer 1

Answer:

x² - 5x + 6 = 0

Step-by-step explanation:

Given---> Sum of two roots of quadratic equation is 5 and sum of their cube is 35.

To find---> Quadratic equation

Solution---> Let roots of quadratic equation be α and β .

ATQ, Sum of roots of quadratic equation is 5

=> α + β = 5

ATQ, Sum of cubes of roots = 35

=> α³ + β³ = 35

=> ( α )³ + ( β )³ = 35

We have an identity , as follows,

( a³ + b³ ) = ( a + b ) ( a² + b² - ab ) , applying it , we get,

=> ( α + β ) ( α² + β² - αβ ) = 35

Adding and subtracting 2αβ in second bracket.

=> ( 5 ) { ( α² + β² + 2αβ ) - 2αβ - αβ } = 35

=> ( α + β )² - 3αβ = 35 / 5

=> ( 5 )² - 3αβ = 7

=> 25 - 3αβ = 7

=> - 3αβ = 7 - 25

=> - 3αβ = - 18

=> 3αβ = 18

=> αβ = 18 / 3

=> αβ = 6

We know that quadratic equation can be represented as

x² - ( Sum of roots ) x + product of roots = 0

=> x² - ( α + β ) x + ( αβ ) = 0

=> x² - ( 5 ) x + 6 = 0

=> x² - 5x + 6 = 0

#Answerwithquality&#BAL

Answer 2

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#answerwithquality #bal