if a and b are the zeroes of x^2 + px -2, then find the value of (a/b +2) (b/a +2)
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Given
- A polynomial
- x²+px-2
- here A and B the roots of this polynomial
To find
- (a/b +2) (b/a +2)
Solution
A+B = -b/a
=>A+B= -p/1
&
A×B=c/a
=>AB= -2
Here A²+B²= (A+B)²-2AB
=>A²+B²=p²+4
Now putting the values
(a/b +2) (b/a +2)
=>a/b×b/a+2(b/a)+2a/b+4
=>5+ 2a²+2b²/ab
=>5+ 2(a²+b²)/ab
=>5+ 2P²+8/-2
=>-5-2P²-8/2
=>-13-2P²/2
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