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29 Dec 2023, 02:30
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63% (02:21) correct
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If both roots of the equation \(x^2-39x+a = 0\) are prime numbers, how many different values of a are there?
A. 1
B. 2
C. 3
D. 4
E. 5
A. 1
B. 2
C. 3
D. 4
E. 5
Both roots of the quadratic equation \(x^2-39x+a = 0\) are prime numbers. How many different possible values of a are there?
29 Dec 2023, 03:11
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From the equation, we know the sum of roots and product of roots:
Sum of roots: 39
Product of roots: a
And both roots are prime numbers and sum is odd, lets go to our basics of number properties : 2 is the only even prime number. so only even+odd= odd.Hence one of the root is 2 and then the other root would be 37.
Hence, only one value possible for a
Sum of roots: 39
Product of roots: a
And both roots are prime numbers and sum is odd, lets go to our basics of number properties : 2 is the only even prime number. so only even+odd= odd.Hence one of the root is 2 and then the other root would be 37.
Hence, only one value possible for a
General Discussion
29 Dec 2023, 11:19
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List all prime number less than \(39\), i.e.\( 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37\). Now, find a pair which sum up to 39. The only pair is \(2, 37\) which sums to \(39\). Hence, only a single value i.e. \(2 \times 37 = 74\).
A
Tip: When \(x^2\) is single or no numeric value (I don't know what to call it), then only one possible answer is available for a.
A
Tip: When \(x^2\) is single or no numeric value (I don't know what to call it), then only one possible answer is available for a.
