Question

if alpha beta are the roots of the equation 2 X square + 3 x minus 4 is equals to zero then the equations whose roots are 3 alpha + 4 beta and 4 alpha + 3 Beta is​

Answer 1

Answer:

x² - 4x + 4 = 0

Step-by-step explanation:

Given-----> α and β are the roots of a quadratic equation , x² -3x + 5 = 0

To find-----> Find the equation whose roots are

( α² - 3α +7 ) and ( β² - 3β + 7 ) .

Solution----> ATQ,

x² - 3x + 5 = 0 .....................( 1 )

Roots are α and β so satisfying equation ( 1 ) by α and β .

α² - 3α + 5 = 0

β² - 3β + 5 = 0

Now we have to find equation whose roots are

( α² - 3α + 7 ) and ( β² - 3β + 7 )

Now ,

( α² - 3α + 7 ) = ( α² - 3α + 5 ) + 2

Putting ( α² - 3α + 5 ) = 0 , in it we get,

= ( 0 ) + 2

=> α² - 3α + 7 = 2

Similarly ,

β² - 3β + 7 = 2

Now , Sum of roots = ( α² - 3α +7 ) + ( β² - 3β + 7 )

= 2 + 2

= 4

Product of roots = ( α² - 3α + 7 ) ( β² - 3β + 7 )

= ( 2 ) ( 2 )

= 4

Now required equation is ,

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

=> x² - ( 4 ) x + 4 = 0

=> x² - 4x + 4 = 0

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