Question

if one root of the equation x²+px+ q=0 if 3 times the other than prove yhat 3p²=16 q​

Answer 1

Answer:

Step-by-step explanation:

Let the zeroes of equation are a and b

According to question

a=3b

Sum of zeroes=

-coefficient of x/coefficient of x²

a+b = -p/1

3b+b = -p

4b= -p

b= -p/4 ---------1

Product of zeroes=

constant/coefficient of x²

a×b = q/1

3b×b = q

3b² = q

Put value of b

3(-p/4)²=q

3(p²/16)=q

3p²=16q

Hence proved

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