if(a-b) a(a+b)are the zeroes of polynomial x3-6x2+9x+5 the value of a is _
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Given cubic polynomial is
p(x)=x3−6x2+3x+10
The zeros of the polynomial p(x) are of the form a, a+b and a+2b
Then,
a+a+b+a+2b=−1−6
=>3a+3b=6
=>a+b=2 ----------------(i)
Also, a(a+b)+(a+b)(a+2b)+a(a+2b)=13
=>a2+ab+a2+2ab+ab+2b2+a2+2ab=3
=>3a2+2b2+6ab=3 ----(ii)
and a(a+b)(a+2b)=−1−10
=>a3+a2b+2a2b+2ab2=10
From (i), b=2−a
Putting this value in (ii), we get
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Given cubic polynomial is
p(x)=x3−6x2+3x+10
The zeros of the polynomial p(x) are of the form a, a+b and a+2b
Then,
a+a+b+a+2b=−1−6
=>3a+3b=6
=>a+b=2 ----------------(i)
Also, a(a+b)+(a+b)(a+2b)+a(a+2b)=13
=>a2+ab+a2+2ab+ab+2b2+a2+2ab=3
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