Given a polynomial equation P(x)=0, which two expressions could be a pair of irrational roots of the equation?
Select two answers.
√2−3
−√2+3
2+√3
√3−2
2−√3
is it √3−2 and −√2+3
Your answers are correct.
M and N are zeros of x^2-5x+6=0 then find value of M+N=
(a) 5
(b) -5
(c) 4
(d) 3
To determine which expressions could be a pair of irrational roots of the polynomial equation P(x) = 0, you need to consider two factors: the presence of irrational numbers and the properties of roots.
Irrational numbers are real numbers that cannot be expressed as a fraction of two integers. They typically involve square roots (√) or other non-repeating decimals.
In this scenario, we have the following choices:
1. √2−3
2. −√2+3
3. 2+√3
4. √3−2
5. 2−√3
To determine which of these expressions could be a pair of irrational roots, we evaluate the given choices:
1. √2−3: This expression involves a square root and a subtraction operation.
2. −√2+3: This expression also involves a square root and a subtraction operation.
3. 2+√3: This expression involves an addition operation, but it includes an irrational number (√3).
4. √3−2: This expression involves a square root, but it also includes a subtraction operation.
5. 2−√3: This expression involves a subtraction operation, but it also includes a square root.
From the given choices, expressions 1 (√2−3) and 2 (−√2+3) are indeed pairs of irrational roots. These expressions feature operations involving square roots and they cannot be simplified into a rational form (a fraction of two integers).
Thus, the correct answer is √2−3 and −√2+3.